Mechanical Properties

185

CHAPTER 6

MECHANICAL PROPERTIES

6.1 MECHANICAL PROPERTIES Polymeric materials are implemented into various designs because of their low cost, processability, and desirable material properties. Of interest to the design engineer are the short- and long-term responses of a loaded component. Properties for short-term responses are usually acquired through short-term tensile tests and impact tests, whereas long-term responses depend on properties measured using techniques such as the creep and the dynamic tests. 6.1.1 The Short-Term Tensile Test The most commonly used mechanical test is the short-term stress-strain tensile test. Stressstrain curves for selected polymers are displayed in Fig. 6.1 [1]. The next two sections discuss the short-term tensile test for elastomers and thermoplastic polymers separately. The main reason for identifying two separate topics is that the deformation of a cross-linked elastomer and an uncross-linked thermoplastic vary greatly. The deformation in a cross-linked polymer is in general reversible, whereas the deformation in typical uncross-linked polymers is associated with molecular chain relaxation, which makes the process time-dependent and is sometimes irreversible.

186

6 Mechanical Properties

100

100

400

T= 22 oC

90

90

80

80

100

70

PC 60

0

PA6

1

2

ε%

3

4

50

PC

PUR Elastomer

ABS

40

Phenolic

0

60

50

PA-Dry

200

PMMA

70

UP-GF 60

300

PA6

40

PP

PP

30

30

PE-LD

PE-HD 20

20

PUR Elastomer

PE-HD

10

10

PE-LD 0

0

0

Figure 6.1:

5

10

15

20

20 20

120 100

220 300 320 400 420 200 Strain (%) ε

520 500

620 600

720 700

820 800

920 1000 900

Tensile stress-strain curves for several materials

Rubber elasticity: The main feature of elastomeric materials is that they can undergo very large and reversible deformations. This is because the curled-up polymer chains stretch during deformation but are hindered from sliding past each other by the cross-links between the molecules. Once a load is released, most of the molecules return to their coiled shape. As an elastomeric polymer component is deformed, the slope of the stress-strain curve drops significantly as the uncurled molecules provide less resistance and entanglement, allowing them to move more freely. Eventually, at deformations of about 400%, the slope starts to increase because the polymer chains are fully stretched. This is followed by polymer chain breakage or crystallization that ends with the fracture of the component. Stress-deformation curves for natural rubber (NR) [2] and a rubber compound [3] composed of 70 parts of styrene-butadiene-rubber (SBR) and 30 parts of natural rubber are presented in Fig. 6.2. Because of the large deformations, typically several hundred percent, the stress-strain data are usually expressed in terms of extension ratio, λ defined by λ=

L , L0

(6.1)

where L represents the instantaneous length and L 0 the initial length of the specimen. Finally, it should be noted that the stiffness and strength of rubber is increased by filling with carbon black. The most common expression for describing the effect of carbon black content on the modulus of rubber was originally derived by Guth and Simha [4] for the viscosity of particle suspensions, and later used by Guth [5] to predict the modulus of filled polymers. The Guth equation can be written as Gf = 1 + 2.5φ + 14.1φ2 , G0

(6.2)

where Gf is the shear modulus of the filled material, G 0 is the shear modulus of the unfilled material, and φ the volume fraction of particulate filler. The above expression is compared to experiments [6, 7] in Fig. 6.3.

6.1 Mechanical Properties

Figure 6.2:

Experimental stress-extension curves for NR and a SBR/NR compound

Figure 6.3:

Effect of filler on modulus of natural rubber

187

The tensile test and thermoplastic polymers: Of all the mechanical tests done on thermoplastic polymers, the tensile test is the least understood, and the results are often misinterpreted and misused. Because the test was inherited from other materials that have linear elastic stress-strain responses, it is often inappropriate for testing polymers. However, standardized tests such as DIN 53457 and ASTM D638 are available to evaluate the stressstrain behavior of polymeric materials. The DIN 53457, for example, is performed at a constant elongational strain rate of 1% per minute,and the resulting data are used to determine the short-term modulus. The ASTM D638 test also uses one rate of deformation per material to measure the modulus; a slow speed for brittle materials and a fast speed for ductile ones. However, these tests do not reflect the actual rate of deformation experienced by the narrow

188

6 Mechanical Properties

portion of the test specimen, making it difficult to maintain a constant speed within the region of interest. The standard tests ASTM D638 and ISO 527-1 are presented in Table 6.1. L3 ≥ 150 mm L2=104 to 113 mm

h=4 ± 0.2 mm

L1=80 ± 2 mm

b2=20 ± 0.2 mm

r= 20 to 25 mm

b1=10 ± 0.2 mm

Figure 6.4:

Standard ISO-3167 tensile bar

LO = 165 mm D=115 ± 5 mm L=57 ± 0.5 mm

T=3.2 ± 0.4 mm

G=50 ± 0.25 mm

WO=19 (+6.4, 0) mm W=13 ± 0.5 mm R= 76 ± 1 mm

Figure 6.5:

Standard ASTM-D638 tensile bar

Table 6.1:

Standard methods of measuring tensile properties (Shastri)

Standard

ISO 527-1:93 and 527-2:93

D638-98

Specimen

ISO 3167 (Type A or B*) multipurpose test specimens (Figure 6.4). * Type A is recommended for directly molded specimens, so the 80 mm x 10 mm x 4 mm specimens required for most tests in ISO 10350-1 can be cut from the center of these specimens. Type B is recommended for machined specimens.

For rigid/semirigid plastics: D638 Type I specimens (Figure 6.5) are the preferred specimen and shall be used when sufficient material having a thickness of 7 mm or less is available.

Continued on next page

6.1 Mechanical Properties

Standard

189

ISO 527-1:93 and 527-2:93

D638-98

Dimensions for ISO 3167 specimens are: Overall Length ⇒ >150 mm Width ⇒ 10 mm Thickness ⇒ 4 mm Fillet radius ⇒ 20-25 mm (Type A) or >60 mm (Type B)

Dimensions for D638 Type I specimens are: Overall Length ⇒ 165 mm Width ⇒ 12.7 mm Thickness ⇒ 3.2 mm Fillet radius ⇒ 76 mm Length of parallel narrow section ⇒ 57 mm Length of parallel narrow section ⇒ 80 mm (Type A) or 60 mm (Type B)

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23 ◦ C ±2 ◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

At 23 ±2 ◦ C and 50 ±5% relative humidity for no less than 40 h prior to testing in accordance with D618 Procedure A for those tests where conditioning is required. For hygroscopic materials, the material specification takes precedence over the above routine preconditioning requirements.

Test procedures

A minimum of five specimens shall be prepared in accordance with the relevant material standard. When none exists, or unless otherwise specified specimens shall be directly compression or injection molded in accordance with ISO 293 or ISO 294-1. Test speed for ductile failure (defined as yielding or with a strain at break >10%) is 50 mm/min and for a brittle failure (defined as rupture without yielding or strain at break < 10%) is 5 mm/min. For modulus determinations the test speed is not specified in ISO 10350; however, in ISO 527-2 it is specified for molding and extrusion plastics that the test speed is 1 mm/min. Extensometers are required for determining strain at yield and tensile modulus.

A minimum of five test specimens shall be prepared by machining operations or die cutting the materials in sheet, plate, slab or similar form. Specimens can also be prepared by injection or compression molding the material to be tested. Test speed is specified in the specification for the material being tested. If no speed is specified, then use the lowest speed (5, 50, or 500 mm/min) which gives rupture within 0.5 to 5.0 minutes. Modulus testing may be conducted at the same speed as the other tensile properties provided that recorder response and resolution are adequate. Extensometers are required for determining strain at yield and tensile modulus. Continued on next page

190

Standard

6 Mechanical Properties

ISO 527-1:93 and 527-2:93

D638-98

The specified initial gauge length is 50 mm. The extensometer shall be essentially free of inertia lag at the specified speed of testing and capable of measuring the change in gauge with an accuracy of 1% of the relevant value or better. This corresponds to ±1 micrometer for the measurement of modulus on a gauge length of 50 mm.

The specified initial gauge length is 50 mm. For modulus determinations, an extensometer which meets Class B-2 (Practice E-38) is required, for low extensions (<20%) the extensometer must at least meet Class C (Practice E38) requirements, for high extensions (>20%) any measurement technique which has an error no greater than ±10% can be used. Tangent modulus is determined by drawing a tangent to the steepest initial straight line portion of the loaddeflection curve and then dividing the difference in stress on any section of this line by the corresponding difference in strain. Secant modulus is the ratio of stress to corresponding strain at any given point on the stress-strain curve, or the slope of the straight line that joins the zero point or corrected zero point and the selected point corresponding to the strain selected on the actual stressstrain curve. Toe compensation, if applicable as defined, is mandatory.

The reported tensile modulus is a chord modulus determined by drawing a straight line that connects the stress at 0.05% strain and the stress at 0.25% strain. There is no requirement for toe compensation in determining a corrected zero point, if necessary.

Values and units

For ductile materials: Stress at yield ⇒ MPa Strain at yield ⇒ % Stress at 50% strain* ⇒ MPa Nominal strain at break** ⇒ % Tensile modulus ⇒ MPa * If the material does not yield before 50% strain, report stress at 50% strain. ** Nominal strain at break based on initial and final grip separations, if rupture occurs above 50% nominal strain one can either report the strain at break or simply > 50%. Stress at break ⇒ MPa Strain at break ⇒ % Chord modulus (0.5–0.25% strain) ⇒ MPa

For ductile materials: Stress at yield ⇒ MPa Strain at yield ⇒ % Stress at break ⇒ MPa Strain at break ⇒ % Tangent modulus or ⇒ MPa Secant modulus ⇒ MPa

Stress at break ⇒ MPa Strain at break ⇒ % Modulus ⇒ MPa

6.1 Mechanical Properties

Figure 6.6:

191

Stress-strain behavior of PMMA at various strain rates

400 Strain rate = 1 Normalized work = 1

N/mm 2

10 0.75

100 mm/min 0.55

300 Strain rate= 100 mm/min

200

10 1

100

0 0

200

400

600

800

1000

%

1200

Strain

Figure 6.7:

Stress-strain behavior of PE at various rates of deformation

However, the rate of deformation has a great impact on the measured results. A typical test performed on PMMA at various strain rates at room temperature is shown in Fig. 6.6. The increased curvature in the results with slow elongational speeds suggests that stress relaxation plays a significant role during the test. Similarly, Fig. 6.7 reflects the effect of rate of deformation on the stress-strain behavior of a typical semicrystalline polymer. The ultimate strength is also affected by the deformation rate, and the trend depends on the polymer, as depicted in Fig. 6.8. Again, the effect is caused by the relaxation behavior of the polymer. The relaxation behavior and memory effects of

192

6 Mechanical Properties

110 22 oC

1002 N/mm

PVC PC

AMMA 90 PMMA 80

CAB

70

ABS

60 PA 6 (2.1% H 20)

PE

50 40

Cross - Linked PUR elastomer Shore - hardness A= 70

30 20 0.01 10 -2

σB 0.1 10 -1

10 10

101 10

100 10 2

1000 10 3

10000 10 4

10 5 %/s 100000

Strain rate

Figure 6.8:

Rate of deformation dependence of strength for various thermoplastics

polymers are illustrated in Fig. 6.9, which shows the strain one minute after the specimen failed for tests performed at different rates of deformation.

100 %

90 PA 6(2.1 % H 20)

80 70 60 50 40 AMMA

PC

30 20 ABS

10

PE

0

0.01 10 -2

0.1 10 -1

10 10

101 10

100 10 2

1000 10 3

PVC CAB

10000 10 4 %/s 100000 10 5

Rate of deformation

Figure 6.9:

Residual strain in the test specimen as a function of strain rate for various thermoplastics

It can be shown that for small strains the secant modulus, described by Es =

σ ,

(6.3)

6.1 Mechanical Properties

Figure 6.10: deformation

193

Schematic of the stress-strain behavior of a viscoelastic material at two rates of

and the tangent modulus, defined by dσ , (6.4) d are independent of strain rate and are functions only of time and temperature. This is schematically shown in Fig. 6.10 [8]. The figure shows two stress-strain responses: one at a slow elongational strain rate, ˙ 1 , and one at twice the speed, defined by ˙ 2 . The tangent modulus at 1 in the curve with ˙ 1 is identical to the tangent modulus at 2 in the curve with ˙ 2 , where 1 and 2 occurred at the same time. For small strains the tangent modulus, E t , is identical to the relaxation modulus, Er , measured with a stress relaxation test. This is important because the complex stress relaxation test can be replaced by the relatively simple short-term tensile test by plotting the tangent modulus versus time. Generic stress-strain curves and stiffness and compliance plots for amorphous and semicrystalline thermoplastics are shown in Fig. 6.11 [9]. The stress-strain behavior for thermoplastic polymers can be written in a general form as Et =

σ = E0

1 − D1 , 1 + D2

(6.5)

where E0 , D1 and D2 are time- and temperature-dependent material properties. The constant D1 = 0 for semi-crystaline polymers and D 2 = 0 for amorphous plastics. Figure 6.12 shows E 0 and D2 for a high-density polyethylene at 23 ◦ C as a function of strain rate. The values of E 0 , D1 and D2 can be easily calculated for each strain rate from the stress-strain diagram [10]. The modulus E 0 simply corresponds to the tangent modulus at small deformations where σ = E0 (6.6) Assuming that for amorphous thermoplastics D 2 ≈ 0 when T  Tg and for semicrystalline thermoplastics D 1 ≈ 0 when T  Tg , we can compute D 1 from D1 =

σ2 1 − σ1 2 σ2 21 − σ1 22

(6.7)

194

6 Mechanical Properties

Figure 6.11: Schematic of the stress-strain response, modulus, and compliance of amorphous and semicrystalline thermoplastics at constant rates of deformation

Figure 6.12:

Coefficients E0 and D2 for a high-density polyethylene at 23 ◦ C

6.1 Mechanical Properties

Figure 6.13:

195

Poisson’s ratio as a function of rate of deformation for PMMA

0.5 PE-LD PA610 0.45 PMMA PE-HD 0.4 PVC-P

PP

0.35 PS -50 oC 0.3 20

40

60

80

100

120

140

o

C

160

Temperature

Figure 6.14:

Poisson’s ratio as a function of temperature for various temperatures

and D2 from D2 =

σ1 2 − σ2 1 .

1 2 (σ2 − σ1 )

(6.8)

Depending on the time scale of the experiment, a property that also varies considerably during testing is Poisson’s ratio, ν. Figure 6.13 [9] shows Poisson’s ratio for PMMA deformed at rates (%/h) between 10 −2 (creep) and 10 3 (impact). Temperature affects Poisson’s ratio in a similar way, as depicted in Fig. 6.14 for several thermoplastics. The limits are ν=0.5 (fluid) for high temperatures or very slow deformation speeds and ν=0.33 (solid) at low temperatures or high deformation speeds. In fiber filled plastics, Poisson’s ratio is affected by the

196

6 Mechanical Properties

0.4 a) EP, unidirectional 0.3 UP, matt a) Loading parallel to fibers b) Loading perpendicular to fibers 0.2

b) 0.1 EP, unidirectional

0 0

10

20

30

40

Fiber fraction (weight)

Figure 6.15:

50

60

70

%

80

ψ

Poisson’s ratio as a function of fiber content for fiber-filled thermosets

fiber content and the orientation of the reinforcing fibers. This is demonstrated in Fig. 6.15 for fiber-filled thermosets. Flexular test: The flexural test is widely accepted in the plastics industry because it accurately portrays bending load cases, which often reflect realistic situations. However, because of the combined tensile and compressive stresses encountered in bending, it is a test that renders properties that should be regarded with caution. The test is summarized for ISO and ASTM standards in Table 6.2. Table 6.2:

Standard methods of measuring flexural properties (Shastri)

Standard

ISO 178

D790 - 98

Specimen

80 mm x 10 mm x 4 mm cut from the center of an ISO 3167 Type A specimen. In any one specimen the thickness within the central one-third of length shall not deviate by more than 0.08 mm from its mean value, and the corresponding allowable deviation in the width is 0.3 mm from its mean value.

Specimens may be cut from sheets, plates, molded shapes or molded to the desired finished dimensions. The recommended specimen for molding materials is 127 mm x 12.7 mm x 3.2 mm.

Continued on next page

6.1 Mechanical Properties

197

Standard

ISO 178

D790 - 98

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23 ◦ C ±2 ◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

At 23 ±2 ◦ C and 50 ±5% relative humidity for not less than 40h prior to testing in accordance with to D618 Procedure A for those tests where conditioning is required. For hygroscopic materials, the material specification takes precedence over the above routine preconditioning requirements.

Apparatus

Support and loading nose radius 5.0 ±0.1 mm (Fig. 6.16) Parallel alignment of the support and loading nose must be less than or equal to 0.02 mm.

Support and loading nose radius 5.0 ±0.1 mm (Fig. 6.17) Parallel alignment of the support and loading noses may be checked by means of a jig with parallel grooves into which the loading nose and supports will fit if properly aligned.

ISO/IEC (see ISO 10350 - 1) Support span length 60 - 68 mm (Adjust the length of the span to within 0.5%, which is 0.3 mm for the span length specified above) Support span to specimen depth ratio 16 ±1; 1 mm/mm

ASTM Methods Support span length* 49.5–50.5 mm (Measure the span accurately to the nearest 0.1 mm for spans less than 63 mm. Use the measured span length for all calculations). Support span to specimen depth ratio 16 (+ 4, -1); 1 mm/mm (specimens with a thickness exceeding the tolerance of ±0.5%).

Test procedures

Test speed ⇒ mm/min

Testing conditions indicated in material specifications take precedence; therefore, it is advisable to refer to the material specification before using the following procedures. Procedure A crosshead speed* ⇒ 1.3 mm/min Procedure B crosshead speed* ⇒ 13 mm/min * Procedure A must be used for modulus determinations, Procedure B may be used for flexural strength determination only Continued on next page

198

Standard

6 Mechanical Properties

ISO 178

D790 - 98

A minimum of five specimens shall be prepared in accordance with the relevant material standard. When none exists, or unless otherwise specified, specimens shall be directly compression or injection molded in accordance with ISO 293 or ISO 294-1. Test specimens that rupture outside the central one-third of the span length shall be discarded and new specimen shall be tested in their place. Measure the width of the test specimen to the nearest 0.1 mm and the thickness to the nearest 0.01 mm in the center of the test specimen. The reported flexural modulus is a chord modulus determined by drawing a straight line that connects the stress at 0.05% strain and the stress at 0.25% strain. There is no requirement for toe compensation in determining a corrected zero point, if necessary.

A minimum of five test specimens are required. No specimen preparation conditions are given.

Measure the width and depth of the test specimen to the nearest 0.03 mm at the center of the support span. Tangent modulus is determined by drawing a tangent to the steepest initial straight line portion of the loaddeflection curve and then dividing the difference in stress on any section of this line by the corresponding difference in strain. Secant modulus is the ratio of stress to corresponding strain at any given point on the stress-strain curve, or the slope of the straight line that joins the zero point and a selected point on the actual stress-strain curve. Toe compensation, if applicable, as defined is mandatory.

Values and units

Flexural modulus ⇒ MPa Flexural strength, at rupture ⇒ MPa Flexural strength, at maximum strain* ⇒ MPa *At conventional deflection which is 1.5 x height: therefore 4 mm specimens would have a maximum strain at 3.5%.

Tangent modulus or ⇒ MPa Secant modulus ⇒ MPa Flexural strength, (at rupture*) ⇒ MPa Flexural yield strength** ⇒ MPa * Maximum allowable strain in the outer fibers is 0.05 mm/mm **The point where the load does not increase with increased deflection, provided it occurs before the maximum strain rate*

6.1 Mechanical Properties

199

F

Loading nose

5o

d = 4 ± 0.2mm

R2= 5 ± 0.1mm

Test specimen

R1= 5 ± 0.1mm Support

L = 60-68mm

l = 80 ± 2mm

Figure 6.16:

Test specimen and fixture for the ISO 178 flexural test

R = 5 ± 0.1mm

R = 5 ± 0.1mm

L = 49.5-50.5 mm

Figure 6.17:

Test specimen and fixture for the ASTM D790 flexural test

200

6 Mechanical Properties

6.1.2 Impact Strength In practice, nearly all polymer components are subjected to impact loads. Since many polymers are tough and ductile, they are often well suited for this type of loading. However, under specific conditions even the most ductile materials, such as polypropylene, can fail in a brittle manner at very low strains. These types of failure are prone to occur at low temperatures and at very high deformation rates. As the rate of deformation increases, the polymer has less time to relax. The limiting point is when the test is so fast that the polymer behaves as a linear elastic material. At this point, fracture occurs at a minimum value of strain, min , and its corresponding stress, σ max . During impact, one should always assume that if this minimum strain value is exceeded at any point in the component, initial fracture has already occurred. Table 6.3 presents minimum elongations at break and corresponding stresses for selected thermoplastics during impact loading. Table 6.3:

Minimum elongation at break and corresponding stress on impact loading Polymers HMW-PMMA

min (%)

σmax (MPa)

2.2

135

PA6+25% SFR

1.8

175

PVC-U

2.0

125

POM

4.0

>130

PC+20% SFR

4.0

>110

PC

6.0

>70

Figure 6.18 summarizes the stress-strain and fracture behavior of a HMW-PMMA tested at various rates of deformation. The area under the stress-strain curves represents the volumespecific energy to fracture (w). For impact, the elongation at break of 2.2% and the stress at break of 135 MPa represent a minimum of volume-specific energy because the stress increases with higher rates of deformation, but the elongation at break remains constant. Hence, if we assume a linear behavior, the minimum volume-specific energy absorption up to fracture can be calculated using wmin =

1 σmax min . 2

(6.9)

The impact strength of a copolymer and polymer blend of the same materials can be quite different, as shown in Fig. 6.19. From the figure it is clear that the propylene-ethylene copolymer, which is an elastomer, has a much higher impact resistance than the basic polypropylene-polyethylene blend. It should be pointed out here that elastomers usually fail by ripping. The ripping or tear strength of elastomers can be tested using the ASTM D1004, ASTM D1938, or DIN 53507 test methods. The latter two methods make use of rectangular test specimens with clean slits cut along the center. The tear strength of elastomers can be increased by introducing certain types of particulate fillers. For example, a well-dispersed carbon black filler can double the ripping strength of a typical elastomer.

6.1 Mechanical Properties

Figure 6.18:

201

Stress-strain behavior of HMW-PMMA at various rates of deformation

Figure 6.19: Impact strength of a propylene-ethylene copolymer and a polypropylene-polyethylene polymer blend

Figure 6.20 shows the effect that different types of fillers have on the ripping strength of a polychloroprene elastomer. In general, one can say if the filler particles are well-dispersed and have diameters between 20 nm and 80 nm, they will reinforce the matrix. Larger particles will act as microscopic stress concentrators and will lower the strength of the polymer component. A case where

6 Mechanical Properties

(MPa)

202

Figure 6.20: Ripping strength of a polychloroprene elastomer as a function of filler content for different types of fillers (Menges)

Figure 6.21:

Tensile strength of PVC as a function of calcium carbonate content (Menges)

the filler adversely affects the polymer matrix is presented in Fig. 6.21, where the strength of PVC is lowered with the addition of a calcium carbonate powder. Impact test: The most common impact tests used to evaluate the strength of polymers are the Izod and the Charpy tests. The Charpy test evaluates the bending impact strength of a small notched or unnotched simply supported specimen that is struck by a swinging hammer. There are notched and unnotched Charpy impact tests. The standard unnotched Charpy impact test is given by the ISO 179 test; however, ASTM does not offer such a test. The ISO 179 test is presented in Table 6.4. The notched Charpy test is done such that the notch faces away from the swinging hammer creating tensile stresses within the notch, as shown in Fig. 6.22. The standard ISO

6.1 Mechanical Properties

203

179 also describes the notched Charpy test, as well as the ASTM D256 and DIN 53453 tests. The standard Charpy notched tests ISO 179 and ASTM D256 are presented in Table 6.5.

0.0025

Figure 6.22:

Schematic of the clamp, specimen, and striking hammer in a Charpy impact test

Table 6.4:

Standard methods of measuring unnotched charpy impact strength (Shastri)

Standard

ISO 179 - 1 and ISO 179 - 2

Specimen

80 mm x 10 mm x 4 mm cut from the center of an ISO 3167 Type A specimen, also referred to as an ISO 179/1eU specimen

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23 ◦ C ±2 ◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

Apparatus

The machine shall be securely fixed to a foundation having a mass at least 20 times that of the heaviest pendulum in use and be capable of being leveled. Continued on next page

204

6 Mechanical Properties

Standard

ISO 179 - 1 and ISO 179 - 2

Apparatus

Striking edge of the hardened steel pendulums is to be tapered to an included angle of 30 ±1◦ and rounded to a radius of 2.0 ±0.5 mm The striking edge of the pendulum shall pass midway, to within ± 0.2 mm, between the specimen supports. The line of contact shall be within ±2◦ of perpendicular to the longitudinal axis of the test specimen. Pendulums with specified nominal energies shall be used: 0.5, 1.0 2.0, 4.0, 5.0, 7.5, 15.0, 25.0, and 50.0 J. Velocity at impact is 2.9 + 10% m/s for the 0.5 to 5.0 J pendulums and 3.8 ±10% m/s for pendulums with energies from 7.5 to 50.0 J. The support anvil’s line of contact with the specimen shall be 62.0 (+0.5, -0.0) mm.

Test procedures

A minimum of ten specimens shall be prepared in accordance with the relevant material standard. When none exists, or unless otherwise specified, specimens shall be directly compression or injection molded in accordance with ISO 293 or ISO 294-1. Edgewise impact is specified. Consumed energy is 10 to 80% of the pendulum energy, at the corresponding specified velocity of impact. If more than one pendulum satisfies these conditions, the pendulum having the highest energy is used. (It is not advisable to compare results obtained using different pendulums). Maximum permissible frictional loss without specimen: 0.02% for 0.5 to 5.0 J pendulum 0.04% for 7.5 J pendulum 0.05% for 15.0 J pendulum 0.10% for 25.0 J pendulum 0.20% for 50.0 J pendulum Permissible error after correction with specimen: 0.01 J for 0.5, 1.0, and 2.0 J pendulums. No correction applicable for pendulums with energies > 2.0 J. Four types of failure are defined as: C – Complete break; specimen separates into one or more pieces. H – Hinge break; an incomplete break such that both parts of the specimen are only held together by a thin peripheral layer in the form of a hinge. P – Partial break; an incomplete break which does meet the definition for a hinge break. NB – Non-break; in the case of the non-break, the specimen is only bent and passed through, possibly combined with stress whitening. Continued on next page

6.1 Mechanical Properties

205

Standard

ISO 179 - 1 and ISO 179 - 2

Values and units

The measured values of complete and hinged breaks can be used for a common mean value with remark. If in the case of partial breaks a value is required, it shall be assigned with the letter P. In case of non-breaks, no figures are to be reported. (If within one sample the test specimens show different types of failures, the mean value for each failure type shall be reported). Unnotched Charpy impact strength ⇒ kJ/m2 .

Table 6.5:

Standard methods of measuring notched charpy impact strength (Shastri)

Standard

ISO 179 - 1 and ISO 179 - 2

D256 - 97

Specimen

80 mm x 10 mm x 4 mm cut from the center of an ISO 3167 Type A specimen with a single notch A, also referred to as an ISO 179/1eA specimen. (see Figure 6.23). Notch A has a 45◦ ±1◦ included angle with a notch base radius of 0.25 ±0.05 mm. The notch should be at a right angle to the principal axis of the specimen. The specimens shall have a remaining width of 8.0 ±0.2 mm after notching. These machined notches shall be prepared in accordance with ISO 2818.

124.5 to 127 mm x 12.7 mm x (*) mm specimen, * The width of the specimens shall be between 3.0 and 12.7 mm as specified in the material specification, or as agreed upon as representative of the crosssection in which the particular material may be used. (Figure 6.24). A single notch with 45◦ ±1◦ included angle with a radius of curvature at the apex 0.25 ±0.05 mm. The plane bisecting the notch angle shall be perpendicular to the face of the test specimen within 2◦ The depth of the plastic material remaining in the bar under the notch shall be 10.16 ±0.05 mm. The notches are to be machined.

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23◦ C ±2◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

At 23◦ C ±2 ◦ C and 50 ±5% relative humidity for not less than 40h prior to testing in accordance with D618 Procedure A for those tests where conditioning is required. For hygroscopic materials, the material specification takes precedence over the above routine preconditioning requirements. Continued on next page

206

6 Mechanical Properties

Standard

ISO 179 - 1 and ISO 179 - 2

D256 - 97

Apparatus

The machine shall be securely fixed to a foundation having a mass at least 20 times that of the heaviest pendulum in use and be capable of being leveled. Striking edge of the hardened steel pendulums is to be tapered to an included angle of 30◦ ±1◦ and rounded to a radius of 2.0 ±0.5 mm.

The machine shall consist of a massive base.

Pendulums with the specified nominal energies shall be used: 0.5, 1.0, 2.0, 4.0, 5.0, 7.5, 15.0, 25.0, and 50.0 J.

Velocity at impact is 2.9 ±10% m/s for the 0.5 to 5.0 J pendulums and 3.8 ±10% m/s for pendulums with energies from 7.5 to 50.0 J. The support anvils line of contact with the specimen shall be 62.0 (+0.5, 0.0) mm.

Test procedures

A minimum of ten specimens shall be prepared in accordance with the relevant material standard. When none exists, or unless otherwise specified, specimens shall be directly compression or injection molded in accordance with ISO 293 or ISO 294-1. Edgewise impact is specified (Figure 6.23). Consumed energy is 10 to 80% of the pendulum energy, at the corresponding specified velocity of impact. If more than one pendulum satisfies these conditions, the pendulum having the highest energy is used. (It is not advisable to compare results obtained using different pendulum)

Striking edge of hardened steel pendulums is to be tapered to an included angle of 45◦ ±2◦ and rounded to a radius of 3.17 ±0.12 mm. Pendulum with an energy of 2.710 ±0.135 J is specified for all specimens that extract up to 85% of this energy. Heavier pendulums are to be used for specimens that require more energy; however, no specific levels of energy pendulums are specified. Velocity at impact is approximately 3.46 m/s, based on the vertical height of fall of the striking nose specified at 610 + 2 mm. The anvils line of contact with the specimen shall be 101.6 ±0.5 mm.

At least five, preferably 10 specimens shall be prepared from sheets, composites (not recommended), or molded specimen. Specific specimen preparations are not given or referenced. Edgewise impact is specified (Figs. 6.22 and 6.26).

Continued on next page

6.1 Mechanical Properties

Standard

Values and units

207

ISO 179 - 1 and ISO 179 - 2

D256 - 97

Maximum permissible frictional loss without specimen: 0.02% for 0.5 to 5.0 J pendulum 0.04% for 7.5 J pendulum 0.05% for 15.0 J pendulum 0.10% for 25.0 J pendulum 0.20% for 50.0 J pendulum Permissible error after correction with specimen: 0.01 J for 0.5, 1.0, and 2.0 J pendulums. No correction applicable for pendulums with energies > 2.0 J. Four types of failure are defined as: C – Complete break; specimen separates into two or more pieces. H – Hinge break; an incomplete break such that both parts of the specimen are only held together by a thin peripheral layer in the form of a hinge. P – Partial break; an incomplete break which does not meet the definition for a hinge break. NB – Non-break; in the case of the non-break, the specimen is only bent and passed through, possibly combined with stress whitening.

Windage and friction correction are not mandatory; however, a method of determining these values is given.

The measured values of complete and hinged breaks can be used for a common mean value with remark. If in the case of partial breaks a value is required, it shall be signed with the letter P. (If within one sample the test specimens show different types of failures, the mean value for each failure type shall be reported.) Notched Charpy impact strength ⇒ kJ/m

Four types of failure are specified: C – Complete break; specimen separates into two or more pieces. H – Hinge break; an incomplete break such that one part of the specimen cannot support itself above the horizontal when the other part is held vertically (less than 90◦ included angle). P – Partial break; an incomplete break which does not meet the definition for a hinge break, but has fractured at least 90% of the distance between the vertex of the notch and the opposite side. NB – Non-break; an incomplete break where the fracture extends less than 90% of the distance between the vertex of the notch and the opposite side.

Only measured values for complete breaks can be reported. (If more than one type of failure is observed for a sample material, then report the average impact value for the complete breaks, followed by the number and percent of the specimen failing in that manner suffixed by the letter code.) Notched Charpy impact strength ⇒ J/m

208

6 Mechanical Properties

L = 80 ± 2mm R = 1 ± 0.1mm

b = 4 ± 0.2mm

45o ± 1o

5o

5o bN = 8 ± 0.2mm

b = 10 ± 0.2mm Direction of impact R = 0.25 ± 0.05mm (Type A notch)

30o ± 1o

Figure 6.23:

Dimensions of Charpy impact test with support and striking edge for ISO 179

C = 60.3-63.5mm 45o ± 1o

A = 10.16 ± 0.05mm E = 12.7 ± 0.15mm R = 0.25 ± 0.05mm

Figure 6.24:

Dimensions of Charpy impact test specimen ASTM D256

The Izod test evaluates the impact resistance of a cantilevered, notched bending specimen as it is struck by a swinging hammer. Figure 6.25 shows a typical Izod-type impact machine, and Fig. 6.26 shows a detailed view of the specimen, the clamp, and the striking hammer. The standard test method that describes the Izod impact test is also the ASTM-D 256 test. The Izod and Charpy impact tests impose bending loads on the test specimens. For tensile impact loading one uses the standard tensile impact tests prescribed by tests ISO 8256 and ASTM D1822 presented in Table 6.6.

6.1 Mechanical Properties

Figure 6.25:

Cantilever beam Izod impact machine

Figure 6.26:

Schematic of the clamp, specimen, and striking hammer in an Izod impact test

209

210

6 Mechanical Properties

L = 80 ± 2mm

Le = 30 ± 2mm 45o ± 1o

x = 6 ± 0.2mm

b = 10 ± 0.5mm

R = 0.25 ± 0.05mm (Type A notch)

Figure 6.27:

Tensile impact specimen (Type 1) for ISO 8256 63.50mm

3.2mm

R=12.7 ± 0.08mm

Type S

3.18 ± 0.03mm 9.35 or 12.71mm

19.05mm

25.4mm 3.2mm

Type L

3.18 ± 0.03mm 27.0mm R=12.7 ± 0.08mm

Figure 6.28:

9.35 or 12.71mm

9.53 ± 0.08mm

Type S and L tensile impact test specimens (ASTM D1822)

Table 6.6:

Standard methods of measuring impact strength (Shastri)

Standard

ISO 8256 : 90

D1822 - 93

Specimen

80 mm x 10 mm x 4 mm, cut from the center of an ISO 3167 Type A specimen, with a double notch. Also referred to as an ISO 8256 Type 1 specimen (Fig. 6.27). Type S or L specimen as specified by this standard (Fig. 6.28). 63.50 mm length x 9.53 or 12.71 mm tab width x 3.2 mm (preferred thickness).

Type S has a non-linear narrow portion width of 3.18 mm, whereas Type L has a 9.53 mm length linear narrow portion width of 3.18 mm.

Continued on next page

6.1 Mechanical Properties

211

Standard

ISO 8256 : 90

D1822 - 93

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23 ◦ C ±2 ◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

At 23 ±2 ◦ C and 50 ±5% relative humidity for not less than 40h, prior to testing in accordance with Practice D618, procedure A. Material specification conditioning requirements take precedence.

Apparatus

The machine shall be securely fixed to a foundation having a mass at least 20 times that of the heaviest pendulum in use and be capable of being leveled. Pendulums with the specified initial potential energies shall be used: 2.0, 4.0, 7.5, 15.0, 25.0, and 50.0 J. Velocity at impact is 2.6 to 3.2 m/s for the 2.0 to 4.0 J pendulums and 3.4 to 4.1 m/s for pendulums with energies from 7.5 to 50.0 J. Free length between grips is 30 ±2 mm. The edges of the serrated grips in close proximity to the test region shall have a radius such that they cut across the edges of the first serrations. Unless otherwise specified in the relevant material standard, a minimum of ten specimens shall be prepared in accordance with that same material standard. When none exists, or unless otherwise specified, specimens shall be directly compression or injection molded in accordance with ISO 293 or ISO 294-1.

The base and suspending frame shall be of sufficiently rigid and massive construction to prevent or minimize energy losses to or through the base and frame. No pendulums specified

Notches shall be machined in accordance with ISO 2818. The radius of the notch base shall be 1.0 ±0.02 mm, with an angle of 45◦ ±1◦ .

Specimens are unnotched.

Test procedures

Velocity at impact is approximately 3.444 m/s, based on the vertical height of fall of the striking nose specified at 610 ±2 mm. Jaw separation is 25.4 mm. The edge of the serrated jaws in close proximity to the test region shall have a 0.40 mm radius to break the edge of the first serrations. Material specification testing conditions take precedence; therefore, it is advisable to refer to the material specification before using the following procedures. At least five, preferably 10, sanded, machined, die cut or molded in a mold with the dimensions specified for Type S and L specimen.

Continued on next page

212

6 Mechanical Properties

Standard

ISO 8256 : 90

Test procedures

The two notches shall be at right angles to its principal axis on opposite sides with a distance between the two notches of 6 ±0.2 mm. The two lines drawn perpendicular to the length direction of the specimen through the apex of each notch shall be within 0.02 mm of each other. The selected pendulum shall consume at least 20%, but not more than 80% of its stored energy in breaking the specimens. If more than one pendulum satisfies these conditions, the pendulum having highest energy is used. Run three blank tests to calculate the mean frictional loss. The loss should not exceed 1% for a 2.0 J pendulum and 0.5% for those specified pendulums with a 4.0 J or greater energy pendulum. Determine the energy correction, using Method A or B, before one can determine the notched tensile impact strength, En . Method AEnergy correction due to the plastic deformation and kinetic energy of the crosshead, Eq Method BCrosshead-bounce energy, Eb . Calculate the notched tensile impact strength, En by dividing the the corrected energy (Method A or B) by the cross sectional area between the two notches.

Values and units

Notched tensile impact strength, En ⇒ kJ/m2

D1822 - 93

Use the lowest capacity pendulum available, unless the impact values go beyond the 85% scale reading. If this occurs, use a higher capacity pendulum.

A friction and windage correction may be applied. A nonmandatory appendix provides the necessary calculations to determine the amount of this type of correction. The bounce correction factor may be applied. A non-mandatory appendix provides the necessary calculations to determine the amount of this correction factor. (A curve must be calculated for the cross head and pendulum used before applying in bounce correction factors). Calculate the corrected impact energy to break by subtracting the friction and windage correction and/or the bounce correction factor from the scale reading of energy to break.

Tensile-impact energy ⇒ J.

Depending on the type of material, the notch tip radius may significantly influence the impact resistance of the specimen. Figure 6.29 presents impact strengths for various thermoplastics as a function of notch tip radius. As expected, impact strength is significantly reduced with decreasing notch radius. Another factor that influences the impact resistance of polymeric materials is the temperature. This is clearly demonstrated in Fig. 6.30, in which PVC specimens with several notch radii are tested at various temperatures. In addition, the impact test sometimes brings out brittle failure in materials that undergo a ductile breakage in a short-term tensile test.

6.1 Mechanical Properties

213

Figure 6.29: Young) [1]

Impact strength as a function of notch tip radius for various polymers (Kinloch and

Figure 6.30: Young) [1]

Impact strength of PVC as a function of temperature and notch tip radii (Kinloch and

Similar to a small notch radius, brittle behavior is sometimes developed by lowering the temperature of the specimen. Figure 6.31 shows the brittle to ductile behavior regimes as a function of temperature for several thermoplastic polymers. Finally, processing conditions, such as barrel temperature during injection molding or extrusion and residence time inside the barrel, can also affect the impact properties of a plastic component. Higher processing temperatures as well as longer residence times will have an adverse effect on impact properties, as depicted for a PA blend in Fig. 6.32.

214

6 Mechanical Properties

Figure 6.31: Brittle to ductile behavior regimes as a function of temperature for several thermoplastic polymers (Crawford) [12]

100 kJ/m 2 90

PA- Blend Ductile

80 70 60 280 oC

290 oC

300 oC

290 oC

Mass temperature

6 min

6 min

6 min

12 min

Residence time in barrrel

50 40 30 20 Brittle fracture 10 0 -60

-40

-20

0

20

40

o

C

60

Test temperature

Figure 6.32: Notched impact strength of a PA blend as a function of test temperature, barrel temperature, and barrel residence time

Another impact test worth mentioning is the falling dart test. This test, described by the ASTM 3029 and DIN 53 453 standard methods, is well suited for specimens that are too thin or flexible to be tested using the Charpy and Izod tests, and when the fracture toughness of a finished product with large surfaces is sought. Figure 6.33 shows a schematic of a typical falling dart test set-up.

6.1 Mechanical Properties

Figure 6.33:

Schematic of a drop weight impact tester

INDUSTRIAL APPLICATION 6.1

PVC Plastic Pipe Failure To illustrate impact failure, an analysis was performed on a failed PVC pipe, shown in Fig. 6.34.

Figure 6.34:

Photo of a PVC plastic pipe failure

215

216

6 Mechanical Properties

To determine the cause of failure, a variety of standard procedures were used. These are: • Visual inspection of the failed part • Material evaluation • Structural finite element analysis A visual inspection of the part indicates that this was a brittle failure. Brittle failures, such as this one, occur rapidly, while ductile failures occur over a longer period of time. In this case study, the pipe was in a cold environment when it failed, at a temperature below -5.0 ◦ C. This temperature is low enough that the impact strength is significantly lowered. Any external force or water hammer effect could have caused the pipe to fail catastrophically. Depending on the quantity or type of plasticizer used, the characteristics of PVC can be dramatically altered to have high impact strength with relatively low hardness and rigidity. Unplasticized PVC pipes are quite rigid with high strength and good chemical resistance. These properties make it attractive for use in above or below ground plumbing applications. However, at reduced temperatures the impact strength of PVC drastically decreases. This means that at low temperatures the ability of PVC to dissipate the energy from a sudden impact is limited and may result in part failure. Figure 6.30 clearly demonstrates how the impact strength of PVC drastically drops at reduced temperatures. One can improve this situation by using a plasticizer that moves the curves in Fig. 6.30 to the left and gives the part a high impact strength at a much lower temperature. However, the gain in one property usually means a compromise of other properties, in this case, a loss in stiffness. One additive that is often used to reduce cost is calcium carbonate, unfortunately, at a significant reduction of impact strength. A reduction in the calcium carbonate added to the base material will significatly improve the impact strength of the PVC pipe. One additive that is often used to reduce cost is calcium carbonate, unfortunately, at a significant reduction of impact strength. A reduction in the calcium carbonate added to the base material will significantly improve the impact strength of the PVC pipe.

Figure 6.35:

Numerical simulation of the PVC pipe failure

Using PVC properties of the used materials, under the given conditions, a finite element analysis was performed. For the analysis the failure of a pipe was simulated

6.1 Mechanical Properties

Figure 6.36:

217

Cross section view of the numerical simulation

using an extreme internal pressure as a condition. The simulated failure of the PVC pipe is presented in the Figs. 6.35 and 6.36. INDUSTRIAL APPLICATION 6.2

Failure of a Polycarbonate Bottle In this application, the screw-top of a polycarbonate bottle failed by cracking. The crack’s initiation site is an important indicator for the root cause of failure, such as: • • • •

high-stress region or stress concentration point presence of impurities, air entrapment or voids caused during manufacturing presence of a knit-line or weld line indication that the plastic was in contact with a corrosive chemical environment that may have led to environmental stress cracking

Analyzing how the crack propagated during failure can help define the mode of failure and consequently the cause of failure: • brittle or ductile failures • fast or slow crack growth • identification of crack growth direction fatigue cracking SEM (Scanning Electron Microscopy) is used first to perform an in-depth analysis of the fractured surfaces. This analysis is also known as fractography. A fractography allows one to locate the initiation site of the crack as well as details about how the crack propagated during failure. The image presented in Fig. 6.37 is a cross-sectional view of the bottle’s threaded region taken with an optical stereomicroscope at a magnification of 10. The failed

218

6 Mechanical Properties

Figure 6.37:

PC bottle threaded region with a magnification of 10

Figure 6.38:

SEM of threaded region with a magnification of 50

surface was gold sputter coated to increase the resolution of the fractography under the SEM. Figure 6.38 presents a magnification of 50 taken under the SEM. Here, multiple crack origins are observed along the inner diameter of the threads. The material exhibits smooth features typical of brittle fracture. Within the mid-wall there is a significant amount of secondary cracking. At high magnification, presented in Fig. 6.39. with a magnification of 900, the crack surfaces show a significant degree of ondulations. These ondulations are the result of absorption or solvation of constituents from the bottle’s fluid into the part. This fractography analysis points to environmental stress cracking (ESC) failure. The extensive secondary cracking and the evidence of chemical absorption suggest that some of the ingredients in the fluid may be inherently aggressive to PC. Contributing factors to the failure are the inherent stress concentration regions at the root of the threads, and usage of a low molecular weight resin to manufacture the bottles. It is very likely that the material grade was substituted during production for one with a higher melt flow index. A possible reason for substitution is an effort of the molder to reduce cost by using a high melt flow index grade that results in lower pressures and shorter cycles. Lower molecular weight PC grade is more susceptible to environmental stress cracking, chemical attack and has lower impact properties. As we continue the trend of outsourcing, material substitution issues will become a mayor factor in part and material quality.

6.1 Mechanical Properties

Figure 6.39:

219

SEM of threaded region with a magnification of 900 50

Dimension change ( μm)

0

-50

10

Figure 6.40:

40

70

100 o Temperature ( C)

130

160

Thermomechanical analysis (TMA) results

To determine possible contributions of residual stresses in the ESC failure, thermomechanical analysis (TMA) tests were conducted on samples in the threaded region of the bottle. There is always a possibility that an important contributor of stress at threaded regions are residual stresses that result from the manufacturing process. TMA measures dimensional change as a function of temperature. High levels of residual stress can appear in the form of an anomalous expansion and contraction of the material around the glass transition temperature. The threaded regions were heated from room temperature to 165 ◦ C. A typical TMA is presented in Fig. 6.40. The samples showed a contraction onset near the glass transition temperature with a secondary expansion before the final contraction. This secondary expansion is evidence of low level residual stresses. These levels are not sufficient to be a major contributing factor in the observed

220

6 Mechanical Properties

failures. This suggests that some combination of the chemicals and tightening stresses are the more important factors that give rise to the cracking in the threaded region of the bottles. INDUSTRIAL APPLICATION 6.3

Stress Failure of a Filter Housing A water filter housing was inspected for failure analysis. The filter’s housing failed at the bottom, as depicted in Fig. 6.41. The failure appears as a circumferential crack that separated the bottom of the housing from the rest of the part. The failure led to extensive water damage in the property where it was installed.

Failure

Figure 6.41:

Water filter failure

When analyzing the stresses and forces on the filter’s housing during operation, two main sources of stresses were identified: (1) a stress originating at the threads of the housing caused by tightening the filter housing to the base, and (2) a stress caused by the internal water pressure. The later was most likely the cause of failure. A finite element structural analysis was performed to determine which areas were exposed to high stress due to internal

6.1 Mechanical Properties

221

water pressure. As Fig. 6.42 reveals, the maximum stresses occur at the inner corner of the bottom cap, the region where the crack originated.

Maximum stress

Figure 6.42:

Simulated stress fields in the water filter housing

The situation was further aggravated by processing defects in the part. Further inspection of the housing revealed there were molding defects and poor material mixing in the region of highest stress. The molding defects were generated during mold filling and they are a source of stress concentrations that can lead to crack initiation. Poor mixing during processing leads to material inhomogeneities that weaken the areas of stress concentrations. The processing defects identified here are contributing factors that led to failure of the filter housing

Molding defects

Poor mixing

Figure 6.43:

Cross-section of the water filter housing

222

6 Mechanical Properties

Ue (J)

Analysis of impact data: Although the most common interpretation of impact tests is qualitative, it is possible to use linear elastic fracture mechanics to quantitatively evaluate impact test results. Using LEFM, it is common to compute the material’s fracture toughness GIC from impact test results. Obviously, LEFM is only valid if the Izod or Charpy test specimen is assumed to follow linear elastic behavior and contains a sharp notch.

Figure 6.44: Elastic energy absorbed at impact fracture as a function of test specimen cross-sectional geometry for a medium-density polyethylene (Plati and Williams) [1]

The Izod or Charpy test specimen absorbs a certain amount of energy, U e , during impact. This energy can be related to the fracture toughness using Ue = GIC tw a,

(6.10)

where t and w are the specimens thickness and width, respectively. The parameter a is a geometric crack factor found in Table 6.7 for various Charpy impact test specimens and in Table 6.8 for various Izod impact test specimens. The elastic energy absorbed by the test specimen during fracture can be represented with energy lost by the pendulum during the test. This allows the test engineer to relate impact test results with the fracture toughness of a material. Figure 6.44 contains both Charpy and Izod test result data for a mediumdensity polyethylene as plots of U e versus tw a with kinetic energy corrections. The fracture toughness is the slope of the curve. Figure 6.45 compares plots of impact-absorbed energy as a function of tw a for unfilled epoxy and epoxies filled with irregular-shaped silica with weight percents of 55% and 64%.

6.1 Mechanical Properties

223

GIC=0.44(kJ/m2)

filled

GIC=0.37(kJ/m2)

GIC=0.24(kJ/m2)

twã (10-5m2)

Figure 6.45: Impact absorbed energy as a function of specimen size for unfilled epoxy and epoxies filled with irregular-shaped silica with weight percents of 55% and 64% Table 6.7:

Charpy impact test geometric crack factors e a 2L/w = 4

2L/w = 6

2L/w = 8 e a

2L/w = 10

2L/w = 12

0.04

1.681

2.456

3.197

3.904

4.580

0.06

1.183

1.715

2..220

2.700

3.155

0.08

0.933

1.340

1.725

2.089

2.432

0.10

0.781

1.112

1.423

1.716

1.990

0.12

0.680

0.957

1.217

1.461

1.688

0.14

0.605

0.844

1.067

1.274

1.467

0.16

0.550

0.757

0.950

1.130

1.297

0.18

0.505

0.688

0.858

1.015

1.161

0.20

0.468

0.631

0.781

0.921

1.050

0.22

0.438

0.584

0.718

0.842

0.956

0.24

0.413

0.543

0.664

0.775

0.877

0.26

0.391

0.508

0.616

0.716

0.808

0.28

0.371

0.477

0.575

0.665

0.748

0.30

0.354

0.450

0.538

0.619

0.694

0.32

0.339

0.425

0.505

0.578

0.647

0.34

0.324

0.403

0.475

0.542

0.603

0.36

0.311

0.382

0.447

0.508

0.564

0.38

0.299

0.363

0.422

0.477

0.527

0.42

0.276

0.328

0.376

0.421

0.462

a/w

Continued on next page

224

6 Mechanical Properties

2L/w = 4

2L/w = 6

2L/w = 8 e a

2L/w = 10

2L/w = 12

0.44

0.265

0.311

0.355

0.395

0.433

0.46

0.254

0.296

0.335

0.371

0.405

0.48

0.244

0.281

0.316

0.349

0.379

0.50

0.233

0.267

0.298

0.327

0.355

0.52

0.224

0.253

0.281

0.307

0.332

0.54

0.214

0.240

0.265

0.88

0.310

0.56

0.205

0.228

0.249

0.270

0.290

0.58

0.196

0.216

0.235

0.253

0.271

0.60

0.187

0.205

0.222

0.238

0.253

2L/w = 12

a/w

Table 6.8:

Izod impact test geometric crack factors e a 2L/w = 4

2L/w = 6

2L/w = 8 e a

2L/w = 10

0.06

1.540

1.744

1.850

2.040

-

0.08

1.273

1.400

1.485

1.675

1.906

0.10

1.060

1.165

1.230

1.360

1.570

0.12

0.911

1.008

1.056

1.153

1.294

0.14

0.795

0.890

0.932

1.010

1.114

0.16

0.708

0.788

0.830

0.900

0.990

0.18

0.650

0.706

0.741

0.809

0.890

0.20

0.600

0.642

0.670

0.730

0.810

0.22

0.560

0.595

0.614

0.669

0.750

0.24

0.529

0.555

0.572

0.617

0.697

0.26

0.500

0.525

0.538

0.577

0.656

0.28

0.473

0.500

0.510

0.545

0.618

0.30

0.452

0.480

0.489

0.519

0.587

0.32

0.434

0.463

0.470

0.500

0.561

0.34

0.420

0.446

0.454

0.481

0.538

0.36

0.410

0.432

0.440

0.468

0.514

0.38

0.397

0.420

0.430

0.454

0.494

0.40

0.387

0.410

0.420

0.441

0.478

0.42

0.380

0.400

0.411

0.431

0.460

0.44

0.375

0.396

0.402

0.423

0.454

a/w

Continued on next page

6.1 Mechanical Properties

225

2L/w = 4

2L/w = 6

2L/w = 8 e a

2L/w = 10

2L/w = 12

0.46

0.369

0.390

0.395

0.415

0.434

0.48

0.364

0.385

0.390

0.408

0.422

0.50

0.360

0.379

0.385

0.399

0.411

a/w

Table 6.9 presents values for stress intensity factor and fracture toughness for several plastics and other materials. Table 6.9: rials

Values of plane stress intensity factor and strain toughness for various mate-

Material

KIC (MN/m3/2 )

GIC (kJ/m2 )

ABS

2–4

5

POM

4

1.2–2

EP

0.3–0.5

0.1–0.3

PE-LD

1

6.5

PE-MD and PE-HD

0.5–5

3.5–6.5

PA66

3

0.25–4

PC

1-2.6

5

UPE-glass reinforced

5–7

5–7

PP-co

3–4.5

8

PS

0.7-1.1

0.3-0.8

PMMA

1.1

1.3

PVC-U

1-4

1.3-1.4

Aluminum-alloy

37

20

Glass

0.75

0.01-0.02

Steel-mild

50

12

Steel-alloy

150

107

Wood

0.5

0.12

6.1.3 Creep Behavior The stress relaxation and the creep test are well-known long-term tests. The stress relaxation test is difficult to perform and is, therefore, often approximated by data acquired through the more commonly used creep test. The stress relaxation of a polymer is often thought of as the inverse of creep. The creep test, which can be performed either in shear, compression, or tension, measures the flow of a polymer component under a constant load. It is a common test that measures the strain, , as a function of stress, time, and temperature. Standard creep

226

6 Mechanical Properties

tests such as ISO 899, ASTM D2990 and DIN 53 444 can be used. The ISO 899 and ASTM D2990, standard creep tests are presented in Table 6.10. Table 6.10:

Standard methods of measuring tensile creep modulus (Shastri)

Standard

ISO 899 - 1

D2990 - 95

Specimen

ISO 3167 Type A specimen

D 638 Type I specimens may be prepared by injection or compression molding or by machining from sheets or other fabricated forms.

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23 ◦ C ±2 ◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

At 23 ±2 ◦ C and 50 ±5% relative humidity for not less than 40h, prior to testing in accordance with D618 Procedure A. The specimens shall be preconditioned in the test environment for at least 48 h prior to testing. Those materials whose creep properties are suspected to be affected by moisture content shall be brought to moisture equilibrium appropriate to the test conditions prior to testing.

Test procedures

Conduct the test in the same atmosphere as used for conditioning, unless otherwise agreed upon by the interested parties, e.g., for testing at elevated or low temperatures.

For material characterization, select two or more test temperatures to cover the useful temperature range. For simple material comparisons, select the test temperatures from the following: 23, 50, 70, 90, 120, and 155 ◦ C. For simple material comparisons, determine the stress to produce 1% strain in 1000 h. Select several loads to produce strains in the approximate range of 1% strain and plot the 1000-h isochronous stress-strain curve* from which the stress to produce 1% strain may be determined by interpolation. * Since only one point of an isochronous plot is obtained from each creep test, it is usually necessary to run at least three stress levels (preferably more) to obtain an isochronous plot. Continued on next page

Select appropriate stress levels to produce data for the application requirements. Where it is necessary to preload the test specimen prior to loading, preloading shall not be applied until the temperature and humidity of the test specimen (finally gripped in the testing apparatus) correspond to the test conditions, and the total load (including preload) shall be taken as the test load.

6.1 Mechanical Properties

Standard

227

ISO 899 - 1

D2990 - 95

Unless the elongation is automatically and/or continuously measured, record the elongations at the following time schedule: 1, 3, 6, 12, and 30 min; 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000 h.

Units

Tensile creep modulus at 1h and at a strain < 0.5% ⇒ MPa Tensile creep modulus at 1000 h and at a strain < 0.5% ⇒ MPa

For creep testing at a single temperature, the minimum number of test specimens at each stress shall be two if four or more stress levels are used or three if fewer than four levels are used. Measure the extension of the specimens in accordance with the approximate time schedule: 1, 6, 12, and 30 min; 1, 2, 5, 50, 100, 200, 500, 700, and 1000 h.

Tensile creep modulus in MPa plotted vs. time in h.

6 %

Stress in MPa

35

24.5 28

T = 23 oC 31.5

4

21

17.5 2

14 10.5 7 3.5

0 0 10 1

1 10

10 2 100

10 3 1000

h

10 4 10000

Time

Figure 6.46:

Creep response of a PBT at 23 ◦ C

Figure 6.46 presents the creep responses of a polybutylene teraphthalate for a range of stresses in a graph with a log scale for time. When plotting creep data in a log-log graph,in the majority of the cases, the creep curves reduce to straight lines as shown for polypropylene in Fig. 6.47. Hence, the creep behavior of most polymers can be approximated with a

228

Figure 6.47:

6 Mechanical Properties

Creep response of a polypropylene plotted on a log-log scale

Power - law model, sometimes referred to as the Norton model, represented by

(t) = k(T )σ n tm ,

(6.11)

where k, n and m are material-dependent properties. Isochronous and isometric creep curves: Typical creep test data, as shown in Fig. 6.46, can be manipulated to be displayed as short-term stress-strain tests or as stress relaxation tests. These manipulated creep-test-data curves are called isochronous and isometric graphs. 40 1h

MPa

100 h

10 h

1000 h

30

10000 h

20

10 T= 23 oC

0 0

2

4

%

6

Strain

Figure 6.48:

Isochronous stress-strain curves for the PBT at 23 ◦ C creep responses shown in Fig. 6.46

An isochronous plot of the creep data is generated by cutting sections through the creep curves at constant times and plotting the stress as a function of strain. The isochronous

6.1 Mechanical Properties

229

curves of the creep data displayed in Fig. 6.46 are presented in Fig. 6.48 [8]. Similar curves can also be generated by performing a series of short creep tests, where a specimen is loaded at a specific stress for a short period of time, typically around 100 s [6]. The load is then removed, and the specimen is allowed to relax for a period of 4 times greater than the time of the creep test. The specimen is then reloaded at a different stress, and the test is repeated until a sufficient number of points exist to plot an isochronous graph. 30

ε0=2%

Stress (MPa)

20

ε0=1% 10 ε0=0.5%

0 10 0

10 1

10 2

10 3

h

10 4

Time

Figure 6.49:

Isometric stress-time curves for the PBT at 23 ◦ C creep responses shown in Fig. 6.46

This procedure is less time-consuming than the regular creep test and is often used to predict the short-term behavior of polymers. However, it should be pointed out that the short-term tests described in the previous section are more accurate, less time consuming, and cheaper to perform. The isometric or "equal size" plots of the creep data are generated by taking constant strain sections of the creep curves and by plotting the stress as a function of time. Isometric curves of the polypropylene creep data presented in Fig. 6.46 are shown in Fig. 6.49 [8]. Creep data can sometimes be presented in terms of secant creep modulus. For this, the data can be generated for a given stress as presented in Fig. 6.50. For specific applications, plastics should also be tested at higher temperatures. To further illustrate the effect temperature has on the mechanical behavior of thermoplastics, Figs. 6.51 and 6.52 present 1000 h isochronous curves for a selected number of thermoplstics at 23 ◦ C and 60 ◦ C, respectively. Creep of thermoplastic polymers can be mitigated by the use of fiber-reinforcements. Figures 6.53 and 6.54 show 1000 h isochronous curves for fiber-reinforced thermoplastics at 23 ◦ C and 60◦ C, respectively.

230

6 Mechanical Properties

2400 MPa 2000 Stress (MPa) 5 1600

10

15 1200 20 800 25

T= 23 oC 400 10 1

10 1 0

10 2 100

10 3 1000

h

10 4 10000

Time

Figure 6.50: Secant creep modulus curves as a function of time for the PBT at 23 ◦ C creep responses shown in Fig. 6.46

45 PES Mpa

PA 66 30 ABS

SAN

PBT

PA 6 PA 12

POM 15

0 0

2

4

%

6

Shear Strain

Figure 6.51:

Isochronous (1000 h) stress-strain curves for selected thermoplastics at 23 ◦ C

6.1 Mechanical Properties

231

45 PES

MPa

30

SAN PA 66 15 ABS

PA 6

POM

PBT

0 0

1.5

3

%

4.5

Strain

Figure 6.52:

Isochronous (1000 h) stress-strain curves for selected thermoplastics at 60 ◦ C

90 PSU PES MPa

PA 66

POM

60

PA 12 PA 6

30

0 0

1

2

%

3

Strain

Figure 6.53: Isochronous (1000 h) stress-strain curves for various fiber-reinforced (25–35 volume %) thermoplastics at 23◦ C

232

6 Mechanical Properties

75 PSU

MPa

PA 66 PBT

50

POM PA 6

25

0 0

1

2

%

3

Strain

Figure 6.54: Isochronous (1000 h) stress-strain curves for various fiber-reinforced (25–35 volume %) thermoplastics at 60 ◦ C

INDUSTRIAL APPLICATION 6.4

Demolding a Safety Cap without Rupturing the Safety Seal

In this case study, an injection molder had extreme difficulties removing a safety cap from the injection mold without damaging the safety seal. Furthermore, the safety seal in those caps that were not damaged during demolding, did not break the first time the bottle was opened, as they should have. The cap undergoes the same mode of deformation during demolding as it does when the bottle is opened for the first time. The purpose of this analysis is to determine if both requirements, not breaking during demolding, and breaking the first time the bottle is opened, can be fullfilled. A solution to the problem may involve a decision of modifying, or not, the mold geometry, as well as adjusting the processing conditions during the injection molding process. The geometry of the cap, cap on the bottle, cap in the mold and demolding of the cap are all presented in Fig. 6.55. As presented in Fig. 6.55 (c) and (d), the safety seal must jump over the barrier ring inside the mold cavity. During this demolding, the threads that support the safety ring must sustain the axial forces generated during demolding. On the other hand, the threads that support the safety ring must break when removing the cap from the bottle (Fig. 6.55(b)). In a simplified form the cap-mold and cap-bottle assembly is shown in Fig. 6.56. The radial force caused by the pressure required to open the ring enough to slide over the barrier ring, or over the screw top of the bottle can be calculated using

6.1 Mechanical Properties

233

Cap geometry

Cap in the mold

Figure 6.55:

Cap on the bottle

Demolding process

Geometry of the cap inside the mold and on the bottle top.

Fr = kEDi2

(6.12)

where, = ΔD/Daverage where ΔD = Dext − Di. The factor k is given by  π(DExt /Di − 1) (DExt /Di )2 − 1 k= 5(DExt /Di )2 (1 − ν) + 5 + 5ν

(6.13)

The radial force is magnified to an axial force, F a , by the friction μ and the angle α using Fa = Fr η

(6.14)

where, η is the magnification factor presented in Fig. 6.57 and given by η=

Fa μ + tan α = Fr 1 − μ tan α

(6.15)

The critical factor here is the modulus, E, of the material at the demolding temperature and at room temperature when opening the bottle. The moduli were calculated

234

6 Mechanical Properties

Fa

DExt α

b Di

Dext

Fa

Figure 6.56:

Simplified geometry of the cap during removal/demolding.

from the 2% secant strain using the 1 hour isochronous stress-strain curves given in Fig. 6.58 for various temperatures. The cap removal forces where calculated using the above equations and the stressstrain curves for the material. These forces were compared to the forces required to break the seal. Figure 6.59 presents these results with the dimensions used for the calculations. The coefficient of friction for the cap removal from the bottle was taken as 0.5, and for the demolding as 0.45, 0.42 and 0.4, for 20, 40 and 60 ◦ C, respectively. The results reveal that for demolding the cap the mold temperature must be as high as possible, where the stresses generated during demolding are lower than the forces required to break the seal. A higher mold temperature will also lead to higher degree of crystallinity, which will contribute to additional ring shrinkage, resulting in higher forces when removing the cap from the bottle. Creep Rupture: During creep, a loaded polymer component will gradually increase in length until fracture or failure occurs. This phenomenon is usually referred to as creep rupture or, sometimes, as static fatigue. During creep, a component is loaded under a constant stress, constantly straining until the material cannot withstand further deformation, causing it to rupture. At high stresses, the rupture occurs sooner than at lower stresses. However, at low enough stresses, failure may never occur. The time it takes for a component or test specimen to fail depends on temperature, load, manufacturing process, environment, etc. It is important to point out that damage is often present and visible before creep rupture

6.1 Mechanical Properties

235 8

μ=0.8

0.6

0.4

0.2

0

7

Magnification factor, η

6 5 4 3 2 1 0 0o

10o

20o

30o

40o

50o

60o

70o

80o

90o

Assembly or disassembly angle, α

Figure 6.57: Force magnification factor as a function of assembly or disassembly angle for various coefficients of friction. 10 40oC 23oC 8

60oC Stress, MPa

6

4

1 hour isochronous curves 2

0 0

1

2

3

Strain, %

Figure 6.58:

Isochronous stress-strain curves for PE-HD at various temperatures.

occurs. This is clearly demonstrated in Fig. 6.60, which presents isochronous creep curves for polymethyl methacrylate at three different temperatures. The regions of linear and nonlinear viscoelasticity and of visual damage are highlighted in the figure. The standard test to measure creep rupture is the same as the creep test. Results from creep rupture tests are usually presented in graphs of applied stress versus the logarithm of

236

6 Mechanical Properties 500 Forces during opening of bottle 400

Forces to break the seal during ejection

Inside mold Di 48.1 mm Dext 49.8 mm DExt 50.4 mm

Force, N

300

200

On bottle 47.6 mm 48.1 mm 50.4 mm

Forces during ejection Forces to break the seal when opening bottle

100

0 20

40

60

Temperature, oC

Calculated results

Figure 6.60:

Isochronous creep curves for PMMA at three different temperatures (Menges) [1]

(MPa)

Figure 6.59:

time to rupture. An example of a creep rupture test that ran for 10 years is shown in Fig. 6.61. Here, the creep rupture of high-density polyethylene pipes under internal pressure was tested at different temperatures. Two general regions with different slopes become obvious in the plots. The points to the left of the knee represent pipes that underwent a ductile failure, whereas those points to the right represent the pipes that had a brittle failure. As pointed out, generating a graph such as the one presented in Fig. 6.61, is an extremely involved and lengthy task that takes several years of testing 1 . Figures 6.62 and 6.63 compare the static fatigue or creep rupture life curves of several thermoplastics at 20 ◦ C and 60 ◦ C, respectively. Since these tests are so time consuming, they are usually only carried out to 1,000 h (6 weeks) and in some cases to 10,000 h (60 weeks). Once the steeper slope, which is typical of the brittle fracture, has been reached, the line can be extrapolated with some degree of confidence to estimate values of creep rupture at future times. 1 These

tests were done between 1958 and 1968 at Hoechst AG, Germany.

6.1 Mechanical Properties

237

20

10 8 6 80 oC

4

2 0.01 10 -2

10 10

65 oC

50 oC

100 10 2

35 oC

10000 10 4

20 oC

1000000 10 6

Time to failure (hrs)

Figure 6.61:

Creep rupture behavior for a high-density polyethylene (Gaube and Kausch) [1]

20 oC

60

POM

MPa PVC-C

PVDF

40 30

PVC-U

PP-H

20 15

PB

ABS

12.5 PP-Cop 10

PE-X

PE-HD (Type 2)

PE-HD

8

6 0.1

1

10

100 Time to fail

Figure 6.62:

1000

10000 1

100000 10

h 1000000 50 Years

Creep rupture behavior of a several thermoplastics at 20 ◦ C

Although the creep test is considered a long-term test, in principle it is difficult to actually distinguish it from monotonic stress strain tests or even impact tests. In fact, one can plot the full behavior of the material, from impact to creep, on the same graph as shown for PMMA under tensile loads at room temperature in Fig. 6.64. The figure represents strain as a function of the logarithm of time. The strain line that represents rupture is denoted by

B . This line represents the maximum attainable strain before failure as a function of time. Obviously, a material tested under an impact tensile loading will strain much less than the

238

6 Mechanical Properties

MPa

60 oC

40 30 20

ABS

15 10

PVDF

POM

PVC-C PP-H PB PVC-U

8 6

PE-X

PE-HD PP-Cop PE-HD (Type 2)

2 0.1

1

10

100 Time to fail

Figure 6.63:

1000

10000

100000

h 1000000

10

50 Years

1

◦

Creep rupture behavior of a several thermoplastics at 60 C

Figure 6.64: Plot of material behavior at room temperature from impact to creep for a PMMA under tensile loads (Menges) [1]

same material tested in a creep test. Of interest in Fig. 6.64 are the two constant stress lines denoted by σ 1 and σ2 . For example, it can be seen that a PMMA specimen loaded to a hypothetical stress of σ 1 will behave as a linear viscoelastic material up to a strain of 1%, at which point the first microcracks start forming or the craze nucleation begins. The crazing appears a little later after the specimen’s deformation is slightly over 2%. The test specimen continues to strain for the next 100 h until it ruptures at a strain of about 8%. From the figure it can be deduced that the first signs of crazing can occur days and perhaps months or years before the material actually fractures. The stress line denoted by σ 2 , where σ1 > σ2 , is a limiting stress under which the component will not craze. Figure 6.64 also demonstrates that a component loaded at high speeds (i.e., impact) will craze and fail at the same strain. A limiting strain of 2.2% is shown. Because these tests take a long time to perform, it is often useful to test the material at higher temperatures, where a similar behavior occurs in a shorter period of time.

6.1 Mechanical Properties

239

Figure 6.65 shows tests performed on PMMA samples at five different temperatures. When comparing the results in Fig. 6.65 to the curve presented in Fig. 6.64, a clear timetemperature superposition becomes visible. In the applied stress versus logarithm of time to rupture curves, such as the one shown in Fig. 6.61, the time-temperature superposition is also evident.

Figure 6.65:

Strain at fracture for a PMMA in creep tests at various temperatures (Menges) [1]

INDUSTRIAL APPLICATION 6.5

Rupture of Water Filled Polyethylene Balls in Ethylene Glycol Water filled high density polyethylene balls packed in an ethylene glycol filled storage tower form part of an air conditioning system. Only three months after the construction of the cooling tower, the polyethylene balls started failing. Figure 6.66 presents the original balls, one ball that was infiltrated by ethylene glycol, and a ball that had cracked and lost the water to the tank.

New Ball

Figure 6.66:

Ball permeated with ethylene glycol

Photographs of the polyethylene balls

Cracked ball

240

6 Mechanical Properties

9.5 MPa FEM results

Loads and thickness distribution

Figure 6.67:

Load case with thickness distribution and FEM calculated stress field

20

10 8 6 80oC

4

2 0.01 -2 10

Figure 6.68:

10 10

100 10 2 Time to failure (hrs)

65 oC

50 oC

10000 104 10 months

35 oC 20 oC

1000000 106

Creep rupture curves for PE-HD

Since the balls are lighter than the ethylene glycol, and the buoyancy forces were known, it was possible to calculate the forces acting on the the balls located at the top of the tank. A sample load case with thickness distribution (left) and stress field (right) is presented in Fig. 6.67. A secant modulus of a 1 year isochronous curve was used in the FEM calculations.

6.1 Mechanical Properties

241

As can be seen, the highest stresses of 9.8 MPa, occurred at the edge of the dimples, the same location where the cracks occurred. It is important to point out here that the ultimate stress of comparable polyethylene materials, measured using ASTM D638 standardized tests, was 18 MPa. However, when comparing the 9.8 MPa stress to creep rupture data for PE-HD, presented in Fig. 6.68, it can be seen that the balls will fail at about 10 months. As is presented in the Industrial Application 8.2 in Chapter 8, the balls were subjected to environmental stress cracking, accelerating the failure from 10 months to only 3 months.

6.1.4 Dynamic Mechanical Tests

Figure 6.69:

Schematic diagram of the torsion pendulum test equipment

The simplest dynamic mechanical test is the torsion pendulum. The standard procedure for the torsional pendulum, shown schematically in Fig. 6.69 [15], is described in DIN 53445 and ASTM D2236. The technique is applicable to virtually all plastics, through a wide range of temperatures; from the temperature of liquid nitrogen, -180 ◦ C, to 50 − 80 ◦ C above the glass transition temperature in amorphous thermoplastics and up to the melting temperature in semicrystalline thermoplastics. With thermoset polymers one can apply torsional tests up to the degradation temperatures of the material. The torsion pendulum apparatus consist of an inertia wheel, grips, and the specimen contained in a temperature-controlled chamber. The rectangular test specimen can be cut from a polymer sheet or part, or it can be made by injection molding. To execute the test, the inertia wheel is deflected, then released and allowed to oscillate freely. The angular displacement or twist of the specimen is recorded over time. The frequency of the oscillations is directly related to the elastic shear modulus of the specimen, G  , and the decay of the amplitude is related to the damping or logarithmic decrement, Δ, of the material. The elastic shear modulus (in Pascals) can be computed using the relation G =

6.4π 2 ILf 2 , μbt3

(6.16)

242

6 Mechanical Properties

where I is the polar moment of inertia (g/cm 2 ), L the specimen length (cm), f the frequency (Hz), b the width of the specimen, t the thickness of the specimen, and μ a shape factor that depends on the width-to-thickness ratio. Values of μ vary between 5.0 for b/t = 10 and 5.333 for b/t = inf [16]. The logarithmic decrement can be computed using   An Δ = Ln , (6.17) An+1 where An represents the amplitude of the nth oscillation. 2Although the elastic shear modulus, G , and the logarithmic decrement, Δ, are sufficient to characterize a material, one can also compute the loss modulus G  by using    GΔ . (6.18) G = π The logarithmic decrement can also be written in terms of loss tangent, tanδ, where δ is the out-of-phase angle between the strain and stress responses. The loss tangent is defined as tanδ =

G Δ = . G π

(6.19)

Because the frequency in the torsional pendulum test depends on the stiffness of the material under consideration, the test’s rate of deformation is also material dependent, and can therefore not be controlled. To overcome this problem, the dynamic mechanical analysis (DM) test, or sinusoidal oscillatory test was developed. In the sinusoidal oscillatory test, a specimen is excited with a predetermined low-frequency stress input, which is recorded along with the strain response. The shapes of the test specimen and the testing procedure vary significantly from test to test. The various tests and their corresponding specimens are described by ASTM D4065 and the terminology, such as the one already used in the above equations, is described by ASTM D4092. If the test specimen in a sinusoidal oscillatory test is perfectly elastic, the stress input and strain response would be in phase, as τ (t) = τ0 = sin ωt

(6.20)

γ(t) = γ0 = sin ωt.

(6.21)

and For an ideally viscous test specimen, the strain response would lag π/2 radians behind the stress input as,  π γ(t) = γ0 = sin ωt + . (6.22) 2 Polymers behave somewhere in between the perfectly elastic and the perfectly viscous materials and their response is described by γ(t) = γ0 = sin ( ωt + δ) . 2 When

Δ > 1, a correction factor must be used to compute G .

(6.23)

6.1 Mechanical Properties

243

The shear modulus takes a complex form of G∗ =

τ (t) τ0 = (cos δ + i sin δ) = G + G , γ(t) γ0

(6.24)

which is graphically represented in Fig. 6.70. G  is usually referred to as storage modulus and G as loss modulus. The ratio of loss modulus to storage modulus is referred to as loss tangent.

Figure 6.70:

Vector representation of the complex shear modulus

Figure 6.71 [1] shows the elastic shear modulus and the loss tangent for various polypropylene grades. In the graph, the glass transition temperatures and the melting temperatures can be seen. The vertical scale in plots such as Fig. 6.71 is usually a logarithmic scale. However, a linear scale better describes the mechanical behavior of polymers in design aspects. Figures 6.72 to 6.75 [1] present the elastic shear modulus on a linear scale for several thermoplastic polymers as a function of temperature. The shear modulus of high temperature application plastics are presented in Fig. 6.76.

Figure 6.71:

Elastic shear modulus and loss factor for various polypropylene grades

244

6 Mechanical Properties

1600 MPa 1400 PS 1200 PMP

1000

SAN

800

PB

400

PE-LD

200

0 -40

SB

PE-HD

600

EVAC -20

0

20

40

60

80

100

120

140

160

180

o 200 C

220

Temperature

Figure 6.72:

Elastic shear modulus for several thermoplastics

1400 MPa 1200

1000

800 PPE PPE+PS

600

PC

PSU

PC+ABS 400 PBT

PET

200

0 -40

-20

0

20

40

60

80

100

120

140

Temperature

Figure 6.73:

Elastic shear modulus for several thermoplastics

160

180

o 200 C

220

6.1 Mechanical Properties

245

1600 PA 66

MPa 1400

PA 6 1200

1000 PA 610 800 PA 12 600

400

200

0 -100

-50

0

50

100

150

200

o

C

250

o

250

Temperature

Figure 6.74:

Elastic shear modulus for several thermoplastics

2200 MPa 2000 1800

POM PAR 25 PPS

PK

1600 1400

PEI PAR 15

1200

PES

1000 800 600 400 200 0 -150

-100

-50

0

50

100

Temperature

Figure 6.75:

Elastic shear modulus for several thermoplastics

150

200

C

246

6 Mechanical Properties

1200 MPa 1000

800 PAEK PSO 600 PC

PES

400

200

0 100

150

200

250

300

o

C

350

Temperature

Figure 6.76:

Elastic shear modulus for several high-temperature application thermoplastics

6.1.5 Fatigue Tests Dynamic loading of any material that leads to failure after a certain number of cycles is called fatigue or dynamic fatigue. Dynamic fatigue is of extreme importance since a cyclic or fluctuating load will cause a component to fail at much lower stresses than it does under monotonic loads. Fatigue testing results are plotted as stress amplitude versus number of cycles to failure. These graphs are usually called S-N curves, a term inherited from metal fatigue testing. Figure 6.77 presents S-N curves for several thermoplastic and thermoset polymers tested at a 30-Hz frequency and at about a zero mean stress, σ m .

Figure 6.77: Stress-life (S-N) curves for several thermoplastic and thermoset polymers tested at a 30-Hz frequency at about a zero mean stress (Riddell)

6.1 Mechanical Properties

247

Figure 6.78: Temperature rise during uniaxial cyclic loading under various stresses at 5 Hz (Crawford) [12]

We must point out here that most fatigue data presented in the literature and in resin supplier data sheets do not present the frequency, specimen geometry, or environmental conditions at which the tests were performed. Hence, such data are not suitable for use in design. The data we present in this section are only intended to illustrate the various problems that arise when measuring fatigue life of a polymer. The information should also serve to reflect trends and as a comparison between various materials and conditions. Fatigue in plastics is strongly dependent on the environment, the temperature, the frequency of loading, the surface, etc. For example, surface irregularities and scratches make crack initiation at the surface more likely in a polymer component that has been machined than in one that was injection molded. An injection molded article is formed by several layers of different orientation. In such parts, the outer layers act as a protective skin that inhibits crack initiation. In an injection molded article, cracks are more likely to be initiated inside the component by defects such as weld lines and filler particles. The gate region is also a prime initiator of fatigue cracks. Corrosive environments also accelerate crack initiation and failure caused by fatigue. Corrosive environments and weathering will be discussed in more detail later in this chapter. It is interesting to point out in Fig. 6.77 that thermoset polymers show a higher fatigue strength than thermoplastics. An obvious cause for this is their greater rigidity. However, more important is the lower internal damping or friction, which reduces temperature rise during testing. Temperature rise during testing is one of the main factors leading to failure when experimentally testing thermoplastic polymers under cyclic loads. The heat generation during testing is caused by the combination of internal frictional or hysteretic heating and low thermal conductivity. At a low frequency and low stress level, the temperature inside the polymer specimen will rise and eventually reach thermal equilibrium when the heat generated by hysteretic heating equals the heat removed from the specimen by conduction. As the frequency is increased, viscous heat is generated faster, causing the temperature to rise even further. This phenomenon is shown in Fig. 6.78, in which the temperature rise during uniaxial cyclic testing of polyacetal is plotted. After thermal equilibrium has been reached, a specimen eventually fails by conventional brittle fatigue, assuming the stress is above the endurance limit. However, if the frequency or stress level is increased even further, the temperature will rise to the point at which the test specimen softens and ruptures before reaching thermal

248

6 Mechanical Properties

Figure 6.79:

Fatigue and thermal failures in acetal tested at 1.67 Hz (Crawford) [12]

Figure 6.80:

Fatigue and thermal failures in acetal tested at various frequencies (Crawford) [12]

equilibrium. This mode of failure is usually referred to as thermal fatigue. This effect is clearly demonstrated in Fig. 6.79. The points marked T denote those specimens that failed because of thermal fatigue. The other points represent the specimens that failed by conventional mechanical fatigue. A better picture of how frequency plays a significant role in fatigue testing of polymeric materials is generated by plotting results such as those shown in Fig. 6.79 for several frequencies (Fig. 6.80). The temperature rise in the component depends on the geometry and size of test specimen. For example, thicker specimens will cool slower and are less likely to reach thermal equilibrium. Similarly, material around a stress concentrator will be subjected to higher stresses that will result in temperatures higher than the rest of the specimen, leading to crack initiation caused by localized thermal fatigue. To neglect the effect of thermal fatigue, cyclic tests with polymers must be performed at very low frequencies that make them much lengthier than those performed with metals and other materials exhibit high thermal conductivity.

6.1 Mechanical Properties

249

48

σ

U

7Hz

N/mm 2

= 1 N/mm

2

48 oC 44 7Hz 54 oC

40 46 oC 7Hz 36

54 oC

52 oC o

58 C 28Hz

21Hz

56 oC

o

74 C

7Hz 53 oC

46 oC 37 oC

3Hz

≈ 30 C o

64 oC

50 oC

≈ 25 C ≈ 28 C o o

32 1000 10 3

10000 10 4

100000 10 5

1000000 10 6

10000000 10 7

Cycles to failure

Figure 6.81: Fatigue curves for a glass fiber-reinforced PA6 tested with three different imposed stress cycles (23 ◦ C)

It is important to understand that although most fatigue data curves state the testing temperature, the resultant data points all have their corresponding temperature at failure. For example, the curves presented in Fig. 6.81 were tested at 23 ◦ C; however, each specimen failed at a different temperature. The curves also illustrate how the shape of the imposed stress cycles affect the fatigue life of the polymer. Stress concentrations have a great impact on the fatigue life of a component. Figures 6.82 and 6.83 compare S-N curves for PVC-U and PA 66, respectively, for specimens with and without a 3-mm circular hole acting as a stress concentrator. Material irregularities caused by filler particles or by weld lines also affect the fatigue of a component. Figures 6.84 and 6.85 compare S-N curves for regular PC and ABS test specimens to fatigue behavior of specimens with a weld line and specimens with a 3-mm circular hole. The previous fatigue graphs pertained to tests with zero mean stress, σ m . However, many polymer components subjected to cyclic loading have other loads and stresses applied to them, leading to non-zero mean stress values. This superposition of two types of loading will lead to a combination of creep, caused by the mean stress, and fatigue, caused by the cyclic stress, σa . Test results from experiments with cyclic loading and non-zero mean stresses are complicated by the fact that some specimens fail because of creep and others because of conventional brittle fatigue. Figure 6.86 illustrates this phenomenon for both cases with and without thermal fatigue, comparing them to experiments in which a simple static loading is applied. For cases with two or more dynamic loadings with different stress or strain amplitudes, a similar strain deformation progression is observed. The strain progression, Δ , is the added creep per cycle caused by different loadings, similar to ratcheting effects in metal components where different loadings are combined. Fiber-reinforced composite polymers are stiffer and less susceptible to fatigue failure. Reinforced plastics have also been found to exhibit lower hysteretic heating effects, making

250

6 Mechanical Properties

Figure 6.82: Fatigue curves for a PVC-U using specimens with and without 3-mm hole stress concentrators tested at 23 ◦ C and 7 Hz with a zero mean stress

Figure 6.83: Fatigue curves for a PA66 using specimens with and without 3-mm hole stress concentrators tested at 23 ◦ C and 7 Hz with a zero mean stress

Figure 6.84: Fatigue curves for a PC using regular specimens and specimens with 3-mm hole stress concentrators and weldlines tested at 23 ◦ C and 7 Hz with a zero mean stress

6.1 Mechanical Properties

251

Figure 6.85: Fatigue curves for ABS (Novodur PH/AT) using regular specimens and specimens with 3-mm hole stress concentrators and weldlines tested at 23 ◦ C and 7 Hz with a zero mean stress

Figure 6.86:

Creep and thermal fatigue effects during cyclic loading

252

6 Mechanical Properties

them less likely to fail by thermal fatigue. Figure 6.87 presents the flexural fatigue behavior for glass fiber-filled and unfilled PA66 tested at 20 ◦ C and a 0.5 Hz frequency with a zero mean stress. Parallel to the fiber orientation, the fatigue life was greater than the life of the specimens tested perpendicular to the orientation direction and the unfilled material specimens.

Figure 6.87: Flexural fatigue curves for a PA66 and a glass fiber-filled polyamide 66 tested at 20 ◦ C and 0.5 Hz with a zero mean stress (Bucknall, Gotham and Vincent) [1]

The fatigue life of the unfilled specimen and the behavior perpendicular to the orientation direction were similar. However, the unfilled material failed by thermal fatigue at high stresses, whereas both the specimens tested perpendicular and parallel to the orientation direction failed by conventional fatigue at high stress levels. Fiber-reinforced systems generally follow a sequence of events during failure consisting of debonding, cracking, and separation.

Figure 6.88: Fatigue curves for a glass-filled polyester mat tested at 20 ◦ C and a frequency of 1.67 Hz (Hertzberg and Mason) [1]

Figure 6.88 clearly demonstrates this sequence of events with a glass-filled polyester mat tested at 20 ◦ C and a frequency of 1.67 Hz. In most composites, debonding occurs after

6.1 Mechanical Properties

253

Figure 6.89: Fatigue curves for a 50% by weight glass fiber-reinforced polyester resin sheet molding compound tested at 23 ◦ C and 93 ◦ C and 10 Hz (Denton) [1]

just a few cycles. It should be pointed out that reinforced polymer composites often do not exhibit an endurance limit, making it necessary to use factors of safety between 3 and 4. The fracture by fatigue is generally preceded by cracking of the matrix material, which gives a visual warning of imminent failure. It is important to mention that the fatigue life of thermoset composites is also affected by temperature. Figure 6.89 shows the tensile strength versus number of cycles to failure for a 50% glass fiber-filled unsaturated polyester tested at 23 ◦ C and 93 ◦ C. At ambient temperature, the material exhibits an endurance limit of about 65 MPa, which is reduced to 52 MPa at 93 ◦ C.

6.1.6 Strength Stability Under Heat Polymers soften and eventually flow as they are heated. It is, therefore, important to know what the limiting temperatures are at which a polymer component can still be loaded with moderate deformations. Figure 6.90 presents the shear modulus as a function of temperature for various thermoplastics with the region of maximum temperature. Three tests are commonly performed on polymer specimens to determine this limiting temperature for a specific material. They are the Vicat temperature test (ISO 306, ASTM D648, and DIN 53460), shown in Fig. 6.91, the heat-distortion temperature (HDT) test (ISO 75 and ASTM D648) shown in Fig. 6.92 and the Martens temperature test (DIN 53458 or 53462). In the Vicat temperature test, a needle loaded with weights is pushed against a plastic specimen inside a glycol bath. This is shown schematically in Fig. 6.91. The uniformly heated glycol bath rises in temperature during the test. The Vicat number or Vicat temperature is measured when the needle has penetrated the polymer by 1 mm. The advantage of this test method is that the test results are not influenced by the part geometry

254

6 Mechanical Properties

2500 Martens Vicat B ISO 75/A Upper limit of acceptable temperature

N/mm 2 2000 PBT

1500

PA 6-GF 30

PC-GF30

1000 PC 500 PA6

0 0

50

100

150

200

oC

250

Temperature

Figure 6.90:

Shear modulus as a function of temperature for several thermoplastics

or manufacturing technique. The practical limit for thermoplastics, such that the finished part does not deform under its own weight, lies around 15K below the Vicat temperature. To determine the heat distortion temperature, the standard specimen lies in a fluid bath on two knife edges separated by a 10-cm distance. A bending force is applied on the center of the specimen. The standard Vicat temperature tests ISO 306 and ASTM D648 are presented in Table 6.11.

Figure 6.91: Apparatus to determine a material’s shape stability under heat using the Vicat temperature test

6.1 Mechanical Properties

Table 6.11:

255

Standard methods of measuring vicat softening temperature (Shastri)

Standard

ISO 306

D1525 - 98

Specimen

10 mm x 10 mm x 4 mm from middle region of the ISO 3167 multipurpose test specimen.

Use at least two specimens to test each sample. The specimen shall be flat, between 3 and 6.5 mm thick, and at least 10 mm x 10 mm in area, or 10 mm in diameter.

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23 ◦ C ±2 ◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

If conditioning of the test specimens is required, then condition at 23 ◦ C ±2 ◦ C and 50 ±5% relative humidity for no less than 40 h prior to testing in accordance with Test Method D618.

Apparatus

The indenting tip shall preferably be of hardened steel 3 mm long, of circular cross section 1.000 ±0.015 mm2 fixed at the bottom of the rod. The lower surface of the indenting tip shall be plane and perpendicular to the axis of the rod and free from burrs. Heating bath containing a suitable liquid (e.g., liquid paraffin, glycerol, transformer oil, and silicone oil) that is stable at the temperature used and does not affect the material under test (e.g., swelling or cracking) in which the test specimen can be immersed to a depth of at least 35 mm is used. An efficient stirrer shall be provided.

A flat-tipped hardened steel needle with a cross-sectional area of 1.000 ±0.015 mm2 shall be used. The needle shall protrud at least 2 mm from the end of the loading rod.

At least two specimens to test each sample.

Use at least two specimens to test each sample. Molding conditions shall be in accordance with the applicable material specification or should be agreed upon by the cooperating laboratories. Continued on next page

Test procedures

Immersion bath containing the heat transfer medium (e.g., silicone oil, glycerine, ethylene glycol, and mineral oil) that will allow the specimens to be submerged at least 35 mm below the surface.

256

Standard

6 Mechanical Properties

ISO 306

D1525 - 98

Specimens tested flatwise. The temperature of the heating equipment should be 20 to 23 ◦ C at the start of each test, unless previous tests have shown that, for the material under test, no error is caused by starting at another temperature. Mount the test specimen horizontally under the indenting tip of the unloaded rod. The indenting tip shall at no point be nearer than 3 mm to the edge of the test specimen. Put the assembly in the heating equipment.

Specimens tested flatwise. The bath temperature shall be 20 to 23 ◦ C at the start of the test unless previous tests have shown that, for a particular material, no error is introduced by starting at a higher temperature. Place the specimen on the support so that it is approximately centered under the needle. The needle should not be nearer than 3 mm to the edge of the test specimen. Lower the needle rod (without extra load) and then lower the assembly into the bath. Apply the extra mass required to increase the load on the specimen to 10 ±0.2 N (Loading 1) or 50 ±1.0 N (Loading 2)

After 5 min, with the indenting tip still in position, add the weights to the load carrying plate so that the total thrust on the test specimen is 50 ±1 N. Set the micrometer dial-gauge reading to zero. Increase the temperature of the heating equipment at a uniform rate: Heating rate ⇒ 50 ±5 ◦ C /h

Values and units

Note the temperature at which the indenting tip has penetrated into the test specimen by 1 ±0.01 mm beyond the starting position, and record it as the Vicat softening temperature of the test specimen.

After waiting five minutes, set the penetration indicator to zero. Start the temperature rise at one of these rates: 50 ±5 ◦ C /h (Rate A) or 120±12 ◦ C/h (Rate B) The rate selection shall be agreed upon by the interested parties. Record the temperature at which the penetration depth is 1 mm. If the range of the temperatures recorded for each specimen exceeds 2 ◦ C , then record the individual temperatures and rerun the test.

Vicat softening temperature ⇒ ◦ C

Vicat softening temperature ⇒ ◦ C

Similar to the Vicat temperature test, the bath’s temperature is increased during the test. The HDT is the temperature at which the rod has bent 0.2 to 0.3 mm (see Fig. 6.92). The Vicat temperature is relatively independent of the shape and type of part, whereas the heatdistortion data are influenced by the shaping and pretreatment of the test sample. Figure 6.93 presents the heat distortion temperature for selected thermoplastics and thermosets as a function of bending stress, measured using ISO 75, and Table 6.12 presents HDT for selected thermoplastics measured using ASTM D648. The standard HDT tests ISO 75 and ASTM D648 are presented in Table 6.13.

6.1 Mechanical Properties

257

Figure 6.92: Apparatus to determine a material’s shape stability under heat using the heat-distortion temperature test (HDT)

In the Martens temperature test, the temperature at which a cantilevered beam has bent 6 mm is recorded. The test sample is placed in a convection oven with a constantly rising temperature. In Europe, the HDT test has replaced the Martens temperature test.

Table 6.12:

Heat distortion temperature for selected thermoplastics Material

HDT(◦ C) 1.86 (MPa)

HDT(◦ C) 0.45 (MPa)

HDPE

50

50

PP

45

120

uPVC

60

82

PMMA

60

100

PA66

105

200

PC

130

145

It is important to point out that these test methods do not provide enough information to determine the allowable operating temperature of molded plastic components subjected to a stress. Heat distortion data are excellent when comparing the performance of different materials and should only be used as a reference, not as a direct design criterion.

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6 Mechanical Properties

240 o C 220

200

PPE+ PS - GF 30

180

PC- GF 40

160

PF, Type 12 140

PC-GF 30 PF, Type 31

120

MF, Type 152

PC

UPE, Type 1140 100

PPE+PS PMMA UF, Type 131.5

80 ABS PVC U PS 60

UPE, Type 1130

CA CAB CP

40

B

A

Process

UPE, Type 1120 Soft

CA CAB CP

C

Hard

20 0

2

4

6

8

10

N/mm 12

2

14

Bending stress σB

Figure 6.93:

Heat distortion temperature for selected thermoplastics as a function of bending stress

6.1 Mechanical Properties

Table 6.13:

259

Techniques for measuring temperature of deflection under load (Shastri)

Standard

ISO 75 - 1 and 75 - 2

D648 - 98c

Specimen

Flatwise ⇒ 80 mm x 10 mm x 4 mm, cut from the ISO 3167 Type A specimen.

Edgewise ⇒ 120 ±10 mm x 12.7 ±0.3 mm x 6.35 mm (5"x1/2"x1/4")

Conditioning

Specimen conditioning, including any post molding treatment, shall be carried out at 23◦ C ±2◦ C and 50 ±5% R.H. for a minimum length of time of 88 h, except where special conditioning is required as specified by the appropriate material standard.

At 23 ◦ C ±2 ◦ C and 50 ±5% relative humidity for not less than 40 h prior to testing in accordance with Procedure A of Method D618.

Apparatus

The contact edges of the supports and the loading nose radius are rounded to a radius of 3.0 ±0.2 mm and shall be longer than the width of the test specimen. Specimen supports should be about 100 mm apart (edgewise specimens). Heating bath shall contain a suitable liquid (e.g., liquid paraffin, glycerol, transformer oil, and silicone oils) that is stable at the temperature used and does not affect the material tested (e.g., swelling, softening, or cracking). An efficient stirrer shall be provided with a means of control so that the temperature can be raised at a uniform rate of 120 K/h ±10 K/h. This heating rate shall be considered to be met if over every 6 min interval during the test, the temperature change is 12 K ±1 K A calibrated micrometer dial-gauge or other suitable measuring instrument capable of measuring to an accuracy of 0.01 mm deflection at the mid point of the test specimen shall be used.

The contact edges of the supports and loading nose shall be rounded to a radius of 3.0 ±0.2 mm. Specimen supports shall be 100 ±2 mm apart, or 64 mm apart (flatwise specimens). Immersion bath shall have a suitable heat-transfer medium (e.g. mineral or silicone oils) which will not affect the specimen and which is safe at the temperatures used. It should be well stirred during the test and provided with means of raising the temperature at a uniform rate of 2 ◦ C ±0.2 ◦ C . This heating rate is met if over every 5 min interval the temperature of the bath shall rise 10 ◦ C ±1 ◦ C at each specimen location.

The deflection measuring device shall be capable of measuring specimen deflection to at least 0.25 mm and is readable to 0.01 mm or better.

Continued on next page

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6 Mechanical Properties

Standard

ISO 75 - 1 and 75 - 2

D648 - 98c

Test procedures

At least two unannealed specimens

At least two specimens shall be used to test each sample at each fiber stress of 0.455 MPa ±2.5% or 1.820 MPa ±2.5%. The bath temperature shall be about room temperature at the start of the test unless previous tests have shown that, for a particular material, no error is introduced by starting at a higher temperature. Apply the desired load to obtain the desired maximum fiber stress of 0.455 MPa or 1.82 MPa to the specimen. Five minutes after applying load, adjust the deflection measuring device to zero/ starting position.

The temperature of the heating bath shall be 20 to 23 ◦ C at the start of each test, unless previous tests have shown that, for the particular materials under test, no error is introduced by starting at other temperatures. Apply the calculated force to give the desired nominal surface stress.

Allow the force to to act for 5 min to compensate partially for the creep exhibited at room temperature when subjected to the specified nominal surface stress. Set the reading of the deflection measuring instrument to zero. Heating rate ⇒ 120 ±10 ◦ C/h Deflections ⇒ 0.32 mm (edgewise) for 10.0 to 10.3 mm height 0.34 mm (flatwise) for height equal to 4 mm. Note the temperature at which the test specimen reaches the deflection corresponding to height of the test specimen as the temperature of deflection under load for the applied nominal surface stress.

Values and units

HDT at 1.8 MPa and (0.45 MPa or 8 MPa) ⇒ ◦ C

Heating rate ⇒ 2.0 ±0.2◦ C/min The deflection when the specimen is positioned edgewise is: 0.25 for a specimen with a depth of 12.7 mm. Record the temperature at which the specimen has deflected the specific amount, as the deflection temperature at either 0.455 MPa or 1.820 MPa.

HDT at 0.455 MPa or 1.820 MPa ⇒ C

◦

References 1. H. Domininghaus. Plastics for Engineers. Hanser Publishers, 1993. 2. L.R.G. Treloar. The Physics of Rubber Elasticity, 3rd. Ed. Clarendon Press, Oxford, 1975. 3. Courtesy ICIPC. Colombia. 4. E. Guth and R. Simha. Kolloid-Zeitschrift, 74(266), 1936. 5. E. Guth. Proceedings of the American Physical Society. Physical Review, 53(321), 1938. 6. H.M. Smallwood. J. Appl. Phys., 15(758), 1944.

6.1 References

261

7. L. Mullins and N.R. Tobin. J. Appl. Polym. Sci., 9(2993), 1965. 8. W. Retting. Rheol. Acta, 8(758), 1969. 9. E. Schmachtenberg. PhD thesis, IKV, RWTH-Aachen, Germany, 1985. 10. M. Weng. PhD thesis, IKV-RWTH-Aachen, Germany, 1988. 11. T. A. Osswald and G. Menges. Material Science of Polymers for Engineers. Hanser Publishers, Munich, 2nd edition, 2003. 12. R.J. Crawford. Plastics Engineering, page 47. Pergamon Press, 2nd edition, 1987. 13. ASTM. Plastics (ii), 08.02,. ASTM Philadelphia, 1994. 14. R.J. Crawford. Rotational Molding of Plastics. Research Studies Press, Somerset, 1992. 15. J.L. O’Toole. Modern Plastics Encyclopedia. McGraw Hill, New York, 1983. 16. L. E. Nielsen. Mechanical Properties of Polymers. Van Nostrand Reinhold, New York, 1962.