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Tensile fracture strength of 2124Al–10 vol.% SiCp composite compact tension specimens
Materials and Design 31 (2010) 2987–2993
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Tensile fracture strength of 2124Al–10 vol.% SiCp composite compact tension specimens T. Parameshwaranpillai a, P.R. Lakshminarayanan b, B. Nageswara Rao c,* a
Faculty of Automobile Engineering, Anna University, Tiruchirappalli 620 024, India Faculty of Manufacturing Engineering, Annamalai University, Chidambaram 608 002, India c Structural Analysis and Testing Group, Vikram Sarabhai Space Centre, Trivandrum 695 022, India b
a r t i c l e
i n f o
Article history: Received 23 October 2009 Accepted 16 January 2010 Available online 22 January 2010
a b s t r a c t This paper examines the tensile fracture behavior of 2124Al–10 vol.% SiCp composites by generating the fracture data from the tensile as well as compact tension specimens. The composites were produced through squeeze casting process. For matrix strengthening and improving ductility, the specimens were heat-treated through solutionizing and ageing. The modified inherent flaw model is utilized for fracture strength evaluation. Fracture strength estimations are found to be in good agreement with test results. The modified relationship between the notched strength and the inherent flaw length will be useful for accurate prediction of the notched tensile strength of composite laminates. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Discontinuously reinforced metal matrix composites, especially particulate reinforced aluminium matrix composites, are currently being used in commercial applications [1–5] because of their high elastic modulus, higher strength and lightweight; the ability to economically produce SiC whiskers, platelets and particulates; the ability to use standard shaping methods such as forging, rolling, extrusion, etc. and much less dependence of the engineering properties on directions than with continuous composites. 2124Al–SiC composites are usually made by powder metallurgy route, avoiding the use of liquid metal, which would produce a brittle reaction zone of Al4C3 around the reinforcement. Prasad and Sasidhara [6] have compiled the flow stress data for 2124 aluminium with varying volume fractions of SiC particulate (15 lm) reinforcements in the vacuum hot pressed and extruded at 500 °C for 30 min. The nominal composition of the matrix (2124Al) in wt.% was 4.2 Cu, 0.99 Mg, 0.72 Mn, 0.16 Fe, 0.13 Si, 0.03 Zn, balance aluminium. 2124AA with 10 vol.% SiCp exhibits large grained matrix structure, which restricts the occurrence of superplasticity due to dynamic recrystallization. The material exhibits flow instability in the temperature range 340–420 °C and at strain rates higher than 1 s1. 2124Al30 vol.% SiCp metal matrix composite is difficult to process because of higher SiCp content. Murty et al. [7] have examined
* Corresponding author. Tel.: +91 471 2565831; fax: +91 471 2564181. E-mail addresses: [email protected] (T. Parameshwaranpillai), prlnau_ [email protected] (P.R. Lakshminarayanan), [email protected] (B. Nageswara Rao). 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.01.032
the hot working characteristics of 2124Al–SiCp metal matrix composites. The mechanical properties of the aluminium metal matrix composites (AlMMCs) generally lie somewhere between those of unreinforced aluminium and titanium alloys. However, it is possible to alter the balance of the properties by careful choice of matrix alloy and level of reinforcement. Experimental studies are made on 2124Al–10 vol.% SiCp composites to examine the influence of heat treatment process parameters on the notched and unnotched tensile strength of the material [8]. These composites were produced through squeeze casting process. Cast metal composites are in general extremely brittle and possessing poor mechanical properties. For matrix strengthening and improving ductility, the specimens were heattreated through solutionizing and ageing. Experiments were done at three different solutionizing temperatures, solutionizing time, ageing temperature and ageing time to examine the influence of heat treatment process parameters on the notched and unnotched tensile strength of the material. Compact tension (CT) specimens with varying crack length, crack mouth width and thickness were tested for evaluation of fracture toughness of the material. The scheme of experiments was planned as per the Taguchi’s design of experiments [9,10]. The fractographs of tensile and CT specimens after the test were performed using scanning electron microscope (SEM). Energy dispersive X-ray analysis at different locations of the fractured specimens indicated chemical composition of the inclusions and matrix constituents. Fractographs in general have the features of intergranular decohesion and transgranular cleavage like fracture. High tensile strength and moderate fracture toughness of the material can be achieved for the heat treatment process parameters: solutionizing at 500 °C for 8 h and aging at 200 °C for 12 h.
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Failure predictions of structural components containing crack like defects through fracture mechanics require mechanical and fracture properties of materials. The extraordinary success of fracture mechanics lies in its ability to combine a theoretical framework with experimentally measured critical quantities. Wu et al. [11] have made a brief review on fracture models for assessing the residual strength of notched fibre metal laminates. The existing analytical models can be categorized into three groups: fracture mechanics models [12,13]; stress–fracture criteria [14–16] and progressive damage models [17–19]. The most notable of fracture models are given by Waddoups et al. [12] and Whitney and Nuismer [14]. Waddoups et al. have applied the classical fracture mechanics to predict the static strength of flawed laminated composites. In their model, intense energy regions characterized by a constant through crack length (aci) and extending symmetrically from each side of the holes on specimens was assumed to define the stress intensity factor. Although the fracture data showed reasonable correlation to their model, the characteristic length (aci) is seen to be not constant but varying. Whitney and Nuismer [14] have, on the other hand proposed the point stress and the average stress criteria. In the former, failure was assumed to occur where the unnotched tensile strength of the material coincided with the notched specimen’s stress distribution. The latter criterion assumes failure when the average value of the stress distribution over a fixed distance near a notch reaches the unnotched tensile strength. The main objective of the progressive damage models is to take into account the damage and resulting changes in the stress distribution that occur throughout the loading process. A basic difficulty that arises is the choice of appropriate combinations of failure modes, failure criteria and property degradation laws. Significant progress is still needed in progressive damage models. Fracture mechanics approach, characteristic distance approach and progressive damage approach are being utilized for notched strength evaluation of composite laminates. Each approach has its own advantages and disadvantages and all are complementary to each other. The objective of this paper is to correlate the fracture data on 2124Al–10 vol.% SiCp composite compact tension (CT) specimens using a modification in the inherent flaw model of Waddoups et al. [12]. The details of modifications made in the inherent flaw model for accurate evaluation of fracture strength of flawed configurations are presented below.
Fig. 1. Inherent flaw length (aci) in a center-crack wide tensile panel.
from Eq. (1) using the notched strength (r1 NC ) for r and c + aci for c. Since aci is unknown, one can obtain by equating these two critical stress intensity factors:
K Q1 ¼ r0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi paci ¼ r1 pðc þ aci Þ NC
ð2Þ
The above equation implies that
c þ aci ¼ aci
r0 r1 NC
2 ð3Þ
The stress intensity factor for a tensile specimen having center crack length (2c) and width (W) under the applied stress (r) is [20]:
KI ¼ r
pffiffiffiffiffiffi pcY
ð4Þ
The finite width correction factor (Y) is 2. Modified inherent flaw model The inherent flaw model consists of a sharp notch from which two intense energy regions are modeled as extended-cracks (similar to the Irwin’s plastic zone correction applied in metals) which have a small but finite length ‘‘aci” (see Fig. 1). The length ‘‘aci” is taken to be the characteristic length of an inherent flaw. For the case of the unnotched tensile specimen, the assumption for the inherent flaw represents the case of a center crack tension specimen having crack length ‘‘2aci”. Waddoups et al. [12] have considered the fracture data of notched and unnotched tensile specimens and estimated the inherent flaw size by equating the respective critical stress intensity factors. The stress intensity factor for a wide tensile specimen having center crack is
pffiffiffiffiffiffi K I ¼ r pc
ð1Þ
Here r is the applied stress and c is half the crack length. The critical stress intensity factor (KQ1) for the unnotched tensile specimen can be obtained from Eq. (1) using r = r0 and c = aci. Here r0 is the unnotched tensile strength. From the fracture data of notched tensile specimen, the value of KQ1 can also be obtained
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pc Y ¼ sec W
ð5Þ
The fracture strength (r1 NC ) of the center-crack wide tensile specimen is obtained from the experimental notched strength (rNC) of the finite width tensile specimen by multiplying the correction factor (Y). Using r1 NC , r0 and c, the unknown characteristic length, aci is found from Eq. (3) as:
( aci ¼ c
r0 r1 NC
)1
2 1
ð6Þ
After determining the characteristic length (aci), the fracture strength (r1 NC ) can be obtained directly from Eq. (3) specifying the crack length (2c). Fracture strength (rNC) of the finite width plate can be obtained by dividing the determined r1 NC with the correction factor, Y. It is noted from the fracture data on different materials that the fracture strength decreases with increase in the crack size. Eq. (6) indicates that the characteristic length (aci) is not a material constant. It increases with increase in the crack size. This calls for a modification in the inherent flaw model.
T. Parameshwaranpillai et al. / Materials and Design 31 (2010) 2987–2993
From the above observations one can write a relation between aci and r1 NC in the non-dimensional form as:
2.2. Compact tension (CT) specimen [20,22]
r1 2 aci ¼ a 1 m NC
c P ; K I ¼ pffiffiffiffiffiffi Y B W W
r0
ð7Þ
The parameters a and m in Eq. (7) are to1 be determined by a r least square curve fit to the data for aci and rNC0 . For the determination of these parameters, two cracked specimen tests in addition to an unflawed specimen test are required; normally more tests are performed to take scatter in test results into account. It should be noted that m = 0 in Eq. (7) represents the case of constant damage size as per the original inherent flaw model [2]. For the case: m > 1 and r1 NC ¼ r0 ;, Eq. (7) results a < 0. Hence, the variation of the parameter in Eq. (7) can be 0 6 m 6 1. Whenever m is found to be greater than unity, the parameter m has to be truncated to one by suitably modifying the parameter a with the fracture data. If m is found to be less than zero, the parameter m has to be truncated to zero and the average of aci values from the fracture data yields the parameter a. Once a and m in Eq. (7) are known, it is possible to eliminate the characteristic length (aci) from the fracture strength Eq. (3). The resulting non-linear equation for the fracture strength (r1 NC ) is
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffi r0 2 r1 c NC ¼ 1 1 m a r1 r0 NC
ð8Þ
This non-linear fracture strength Eq. (8) is solved using the Newton–Raphson iterative scheme to obtain r1 NC for the specified crack size. The fracture strength (rNC) of the finite width plate is obtained by dividing the determined r1 NC with the correction factor (Y). Expressions for the stress intensity factors to Compact tension (CT) specimen and center-cracked tensile specimen (see Fig. 2) useful in fracture analysis are presented below. 2.1. Center-cracked tensile specimen [20,21]
KI ¼
P pffiffiffiffi c pcY BW W
ð9Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where the finite width correction factor, YðnÞ ¼ secðpnÞ; P is the P load; B is the thickness; W is the width; the applied stress, r ¼ BW and c is half the crack length of the specimen.
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ð10Þ 3
where YðnÞ¼ð2þnÞð1nÞ2 ð0:886þ4:64n13:32n2 þ14:72n3 5:6n4 Þ. P is the load; B is the thickness; W is the width and c is crack length of the CT specimen. It should be noted that the value of KQ for the cracked specimens is obtained by substituting the failure load, Pmax for P in the stress intensity factor equations. The fracture strength of the infinitely large width center-cracked tensile specimen is
K
Q r1 NC ¼ pffiffiffiffiffiffi pc
ð11Þ
3. Results and discussion Compact tension (CT) specimens with varying crack length, crack mouth width and thickness were tested for generation of fracture data of the 2124Al–10 vol.% SiCp composites. The scheme of experiments was planned as per the Taguchi’s design of experiments. Tensile strength and fracture toughness properties of the 2124Al–10 vol.% SiCp composite were generated for different heat-treatment conditions [8]. Nine blanks of 50 50 7.5 mm, 50 50 10 mm, 50 50 12 mm were cut from the extrusion at Annamalai University. The blanks were further machined to final dimensions of the CT specimens as per ASTM E399 standards. The specimens were notched in the L–T orientation. Special care was taken while pre-cracking the specimens with fatigue cracks of controlled lengths. Fracture analysis has been carried out on the fracture data of CT specimens made of of 2124Al–10 vol.% SiCp composites. Using the failure load (Pmax) and the dimensions of the CT specimens in Eq. (10), the stress intensity factor (KQ) is obtained. The fracture strength (r1 NC ) of the infinitely large width specimen is obtained from Eq. (11). Using the values of the unnotched strength (r0) and the fracture strength (r1 NC ) in Eq. (6), the inherent flaw length (aci) is estimated. Table 1 gives the inherent flaw length for the fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for the specified heat treatment process parameters: Solutionizing temperature = 500 °C; Solutionizing time = 12 h; Aging temperature = 200 °C; and aging time = 12 h. The parameters a and m in Eq. (7) are determined r1 NC using the data of aci and r0 from Table 1 through a least square curve fit. For the specified crack length, the non-linear fracture strength Eq. (8) is solved using the Newton–Raphson iterative scheme and obtained r1 NC . The stress intensity factor (KQ) is obtained using Eq. (11) and the failure load (Pmax) of the CT specimen is obtained from the stress intensity Eq. (10) by equating KI = KQ and P = Pmax. Table 2 shows a good comparison of failure load estimates of CT specimens following the modified inherent flaw model with the test results. The parameter m in Eq. (7) for the material is found from the fracture data is zero and hence no variation in the inherent flaw size (aci ¼ a ) with increasing the crack size of the specimen at failure. The relative error (%) between the analysis and test results is computed from
Relative error ð%Þ ¼ 100 ½1 ðAnalysis result=Test resultÞ ð12Þ
Fig. 2. Test specimens for notched tensile strength evaluation of the composites: (a) compact tension (CT) specimen and (b) center-cracked tensile specimen.
Table 3 gives the values of inherent flaw length (aci) for the fracture data on 2124Al–10 vol.% SiCp composites generated from
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Table 1 Fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for the specified heat treatment process parameters (solutionizing temperature = 500 °C; solutionizing time = 12 h; aging temperature = 200 °C and aging time = 12 h). Width (W) = 32 mm; tensile strength (r0) = 282 MPa. Crack Length, c (mm)
Thickness, B (mm)
Crack mouth width (mm)
Failure load, Pmax (kN)
r1 NC (MPa) Eq. (11)
Inherent flaw length, aci (mm) Eq. (6)
10 13.33 16 11 14.66 17.6 12 16 19.2
7.5 10 12 7.5 10 12 7.5 10 12
1.2 1.4 1.6 1.4 1.6 1.2 1.6 1.2 1.4
4.953 5.030 4.990 4.956 4.325 4.580 4.241 3.946 3.697
120.9 104.5 100.1 125.0 96.14 103.1 111.0 95.04 95.75
2.253 2.123 2.309 2.689 1.928 2.716 2.200 2.050 2.502
Table 2 Comparison of analytical and experimental fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for the specified heat treatment process parameters (solutionizing temperature = 500 °C; solutionizing time = 12 h; aging temperature = 200 °C; and aging time = 12 h). Width (W) = 32 mm; tensile strength (r0) = 282 MPa; a = 2.301 mm; m = 0. Crack length, c (mm)
Thickness, B (mm)
10 13.33 16 11 14.66 17.6 12 16 19.2
Crack mouth width (mm)
7.5 10 12 7.5 10 12 7.5 10 12
1.2 1.4 1.6 1.4 1.6 1.2 1.6 1.2 1.4
Failure load, Pmax (kN)
Relative error (%)
Test [8]
Analysis
4.953 5.030 4.990 4.956 4.325 4.580 4.241 3.946 3.697
4.996 5.206 4.982 4.651 4.673 4.259 4.322 4.152 3.562
0.9 3.5 0.2 6.2 8.0 7.0 1.9 5.2 3.7
Table 3 Inherent flaw length (aci) for the fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for different heat treatment process parameters as per the orthogonal array L9 (34) of Taguchi. Width (W) = 32 mm; thickness (B) = 7.5 mm; initial crack size (c) = 10 mm. Test runs
1 2 3 4 5 6 7 8 9
Solutionizing
Aging
Temp. (°C)
Time (h)
Temp. (°C)
Time (h)
500 500 500 520 520 520 540 540 540
6 8 10 6 8 10 6 8 10
180 200 220 200 220 180 220 180 200
10 12 14 14 10 12 12 14 10
Tensile strength, r0 (MPa)
Failure load, Pmax (kN)
Inherent flaw length, aci (mm) Eq. (6)
277 335 300 177 222 209 298 314 257
4.294 3.338 3.169 3.784 4.065 3.812 5.800 4.309 5.001
1.672 0.629 0.712 3.744 2.497 2.473 2.916 1.264 2.914
compact tension (CT) specimens for different heat treatment process parameters as per the orthogonal array L9 (34) of Taguchi. It r1 should be noted from Eq. (3) that rNC0 increases with increasing the inherent flaw size (aci) for the specified crack size. From the data of Table 3, it is possible to generate the fracture strength of the CT specimen for the specified crack size and the heat treatment process parameters. The fracture strength decreases with increasing the crack size. It is very interesting to note from the fracture data of Table 3 that the failure load of the CT specimen is maximum for the specified heat treatment process parameters: Solutionizing temperature = 540 °C; Solutionizing time = 6 h; Aging temperature = 220 °C and aging time = 12 h. These process parameters for the material will provide optimum strength and fracture properties. Fibre reinforced metal laminates (FRMLs) are a new family of aerospace structural materials developed for fatigue critical applications. These materials are laminated sheets of thin and high strength metal layers, viz., aramid/epoxy, cabon/epoxy, glass/ epoxy, etc. Lawcock et al. [18] have presented the tensile fracture strength data from the center cracked configuration of carbon fibre
reinforced metal laminates (CFRML), Aramid fibre reinforced aluminium laminates (ARALL-2) and glass fibre reinforced aluminium laminates (GLARE-2). The fracture data generated by Lawcock et al. [18] are useful to understand the fracture behavior of composite laminates containing central cracks. For the case of central crack configurations, the failure load max is used in Eq. (9) and ob(Pmax) or the fracture strength, rNC ¼ PBW tained the stress intensity factor (KQ). The fracture strength (r1 NC ) of the infinitely large width specimen is obtained from Eq. (11). Using the values of the unnotched strength (r0) and the fracture strength (r1 NC ) in Eq. (6), the inherent flaw length (aci) is estimated. The parameters a and m in Eq. (7) are determined using the data of r1 NC aci and r0 through a least square curve fit. For the specified crack length, the non-linear fracture strength Eq. (8) is solved using the Newton–Raphson iterative scheme and obtained r1 NC . The stress intensity factor (KQ) is obtained using Eq. (11) and the failure load (Pmax) of the center crack specimen is obtained from the stress intensity Eq. (9) by equating KI = KQ max and P = Pmax. The fracture strength, rNC ¼ PBW of the center crack tension specimens is obtained.
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Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [18]
Relative error (%) Analysis
Material: carbon fibre reinforced metal laminates (CFRML) (2/1 lay-up of 2024-T3 + ICI fiberite T300/7714A UD CF/epoxy prepeg) r0 = 883.4 MPa; a = 3.092 mm; m = 0.460 90.02 10.29 422.3 447.1 5.9 90.10 10.03 439.4 450.7 2.6 89.94 19.97 361.5 352.2 2.6 89.94 19.81 370.2 353.3 4.5 90.00 30.08 288.6 291.5 1.0 90.12 29.45 306.1 294.8 3.7 90.00 30.04 304.8 291.7 4.3 90.12 29.41 296.3 295.0 0.4 90.04 29.38 302.8 295.1 2.5 90.14 39.99 240.4 246.2 2.4 90.18 40.21 235.7 245.3 4.0 90.10 40.07 237.5 245.8 3.5 Material: aramid fibre reinforced aluminium laminates (ARALL-2) (2/1 lay-up of 2024-T3 + UD aramid prepeg) r0 = 717 MPa; a = 2.1313 mm; m = 0 100 25 217.1 263 3.0 100 50 163.3 169 3.5 Material: glass fibre reinforced aluminium laminates (GLARE-2) (2/1 lay-up of 2024-T3 + UDR – glass prepeg) r0 = 1230 MPa; a = 2.4048 mm; m = 0.460 99.8 25 478.2 474.8 0.7 100 50 304 306.4 0.8
Table 5 Fracture strength of T300 carbon/epoxy center-cracked tensile specimens. Width, W (mm)
Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [23]
Analysis
Relative error (%)
Material: T300 carbon/941C lay-up: ½ð45=0=90Þ3 =0=90= 45S : r0 = 548 MPa; a=2.7483 mm; m = 0 36.2 6 355.7 48.1 8 334.3 60.2 10 350.7 36.3 10 304.7
372.5 343.7 320.8 311.0
4.7 2.8 8.5 2.1
Material: T300 carbon/ N5208 lay-up: ½0=904S : r0 = 636 MPa; a = 8.12 mm; m = 0.71 25.1 2.8 471.9 25.1 7.8 321.2 50.5 15.2 322.5 76.0 25.2 319.3
472.3 373.9 323.0 279.1
0.1 16.4 0.1 12.6
Material: T300 carbon/N5208 lay-up: ½0= 45=902S : r0 = 494 MPa; a = 4.38 mm; 25.3 2.8 25.4 7.8 50.6 15.2 76.2 25.2
427.1 338.3 282.0 233.8
1.4 6.8 1.7 2.2
Table 4 shows a good comparison of analytical and experimental fracture strength of CFRML, ARALL-2 and GLARE-2. Tables 5 and 6 show the comparison of experimental results of Khatibi et al. [23] and estimated notched strength values of carbon/epoxy and glass fibre/epoxy laminates containing central sharp-notches. The parameter m in Eq. (7) for these materials is found from the fracture data is
m=0 433.2 316.7 287.0 239.1
not zero and hence the inherent flaw size (aci) increases with increasing the crack size of the specimen at failure. The fracture strength is found to decrease with increasing the crack size and analytical results are found to be in good agreement with test results. The validity of the modified inherent flaw model is further examined considering the fracture data [24] on carbon/epoxy and
Table 6 Fracture strength of Scotchply 1002 center-cracked tensile specimens. Width, W (mm)
Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [23]
Analysis
Relative error (%)
Lay-up: ½0= 45=902S : r0 = 320 MPa; a=2.486 mm; m = 0.272 25.0 2.9 25.2 7.7 50.6 14.7 76.0 24.8
226.2 173.8 140.8 108.2
229.9 169.6 137.7 111.5
1.6 2.4 2.2 3.0
Lay-up: ½0=904S : r0 = 422.6 MPa; a = 1.8308 mm; m = 0.363 25.2 2.6 25.0 7.2 50.6 14.9 76.0 25.8
272.6 203.8 170.1 116.1
280.7 201.8 156.5 124.1
3.0 1.0 8.0 6.9
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glass/polyester composites. Table 7 shows a good comparison of analytical and experimental failure loads of CT specimens made of carbon/epoxy. Table 8 shows excellent match of analytical failure loads with test results [24] of center-cracked tensile specimens made of glass/polyester. Boron/aluminium composites are considered for numerous applications, such as jet engine fan blades, landing gears, transmission housing, other aircraft structures, missiles, and aerospace vehicles [25]. Table 9 shows a good comparison of the present fracture analysis results with experimental failure loads [26] of boron/aluminium laminates in symmetric lay-ups of ½45 =02 S containing center notch. The parameter m in Eq. (7) for the materials in Tables 7–9 is found from the fracture data is zero and hence no variation in the inherent flaw size (aci ¼ a ) with increasing the crack size of the specimen at failure. The fracture strength is found to decrease with increasing the crack length. Polymeric composite materials are widely used in automotive applications for reducing structural weight, saving fuel, and improving performance. Accidental impact damage is an important issue in the use of these composite materials as body components. The damages or cracks in the experimental work of Khashaba [27] were represented by notched specimens, which were fabricated from polyester resin reinforced by woven E-glass fibre. The parameter m in Eq. (7) from the fracture data of this material in Table 10 is found to be non-zero and hence variation in the inherent flaw size (aci) can be expected with increasing the crack size of the specimen at failure. Table 10 shows a good comparison of notched tensile strength values of the modified inherent fracture model with Table 7 Comparison of analytical and experimental failure loads of CT specimens made of carbon/epoxy. Width (W) = 80 mm; tensile strength (r0) = 581 MPa; a = 1.583 mm; m = 0. Crack length, c (mm)
28 36 44 52
max (MPa) Fracture strength = PBW
Test [24]
Analysis
22.3 17.4 12.9 8.5
21.8 16.8 12.4 8.4
Test [24]
Analysis
18 27 36
74.9 60.3 52.7
73.8 61.7 52.4
Relative error (%)
1.5 2.2 0.5
Table 9 Comparison of analytical and experimental failure loads of boron/aluminium laminates in symmetric lay-ups of ½45 =02 S containing center notch. Tensile strength (r0) = 848.1 MPa; a = 1.1232 mm; m = 0. Width, W (mm)
25.35 24.56 25.68 25.20 25.83 25.27
Crack length, 2c (mm)
6.68 6.35 6.38 8.00 7.98 7.98
Fracture max strength = PBW (MPa)
Test [26]
Analysis
406.8 420.6 413.7 372.3 358.5 386.1
407.1 415.6 416.2 372.2 373.9 372.8
Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [27]
Analysis
Relative error (%)
30.9 30.9 30.9 30.9
6 9 12 15
126.6 104.2 87.7 77.2
126.10 104.63 88.98 76.10
0.4 0.4 1.5 1.4
test results [27]. The fracture strength is found to decrease with increasing the crack size.
4. Conclusions Notched tensile strength of 2124Al–10 vol.% SiCp composites is evaluated in this paper considering the fracture data of the material generated from the compact tension (CT) specimens and following the modified inherent flaw model. Fracture strength estimations are found to be in good agreement with test results. The validity of the modified inherent flaw model is examined considering the fracture data of CT specimens as well as center crack tension specimens made of different fibre reinforced metal laminates. For other cracked configurations, one has to find the stress intensity factor solutions and use the inherent flaw model with the modified relationship between the notched strength and the inherent flaw length for accurate prediction of the notched tensile strength of composite laminates.
References
Table 8 Comparison of analytical and experimental failure loads of center-cracked tensile specimens made of glass/polyester. Width (W) = 90 mm; tensile strength (r0) = 135 MPa; a = 4.126 mm; m = 0. max (MPa) Fracture strength = PBW
Width, W (mm)
Relative error (%)
2.5 3.6 4.3 1.8
Crack length, 2c (mm)
Table 10 Comparison of notched tensile strength of GFRP specimens having center cracks (r0 = 291.3 MPa; a=0.8954 mm; m = 0.215).
Relative error (%)
0.1 1.2 0.6 0.0 4.3 3.4
[1] Zhong L. Deformation behavior and microstructure effect in 2124Al/SiCp composite. J Compos Mater 2000;34:101–15. [2] Satyanarayana KG, Pillai RM, Pai BC. Recent developments and prospects in cast aluminium matrix composites. Trans Indian Inst Met 2002;55:15–130. [3] Pai BC, Rajan TPD, Pillai RM. Aluminium matrix composite castings for automotive applications. Indian Foundry J 2004;50:30–9. [4] Korkut MH. Effect of particulate reinforcement on wear behaviour of aluminium matrix composites. Mater Sci Technol 2004;20:73–81. [5] Cantor Brain, Dunne Fionn, Stone Ian. Metal and ceramic matrix composites, series in materials science and engineering. Bristol: IOP Publishing Ltd.; 2004. [6] Prasad YVRK, Sasidhara S. Hot working guide – a compendium of processing maps. OH, USA: ASM Metals Park; 1997. [7] Murty SVSN, Nageswara Rao B, Kashyap BP. On the hot working characteristics of 2124Al–SiCp metal matrix composites. Adv Compos Mater 2002;11:105–20. [8] Parameshwaranpillai T, Lakshminarayanan PR, Nageswara Rao B. Fracture behavior of 2124Al–10 vol.% SiCp composite tensile specimens for different heat treatment conditions. Communicated for Publication in Materials & Design Journal (Ms. No.: JMAD-D-09-01483). [9] Taguchi G. System of experimental design. New York: Kraus International Publications; 1987. [10] Ranjit KR. A primer on the Taguchi method. Dearborn, Michigan: Society of Manufacturing Engineers; 1990. p. 42–125. [11] Wu Guocai, Tan Yi, Yang Jenn-Ming. Evaluation of residual strength of notched fiber metal laminates. Mater Sci Eng, A 2007;457:338–49. [12] Waddoups ME, Eisenman JR, Kaminski BE. Macroscopic fracture mechanics of advanced composite materials. J Compos Mater 1971;5:446–51. [13] Beaumont P. The failure of fibre composites: an overview. Journal of Strain Analysis 1989;24:189–205. [14] Whitney J, Nuismer R. Stress fracture criteria for laminated composites containing stress concentrations. J Compos Mater 1974;8:253–65. [15] Kim JK, Kim DS, Takeda N. Notched strength and fracture criterion on fabric composite plates containing a circular hole. J Compos Mater 1995;29:982–98. [16] Tercan M, Asi O, Aktas A. Determination of critical crack length of notched weft-knitted glass fiber variable width composite plates. Compos Struct 2007;77:111–9. [17] Naik NK, Shembekar PS. Notched strength of fabric laminates: I. Prediction. Compos Sci Technol 1992;44:1–12. [18] Lawcock G, Ye L, Mai YW. Progressive damage and residual strength of carbon fibre reinforced metal laminate. J Compos Mater 1997;31:762–87. [19] Hallett SR, Wisnom MR. Numerical investigation of progressive damage and the effect of lay-up in notched tensile tests. J Compos Mater 2006;40:1229–45.
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Technical Report
Tensile fracture strength of 2124Al–10 vol.% SiCp composite compact tension specimens T. Parameshwaranpillai a, P.R. Lakshminarayanan b, B. Nageswara Rao c,* a
Faculty of Automobile Engineering, Anna University, Tiruchirappalli 620 024, India Faculty of Manufacturing Engineering, Annamalai University, Chidambaram 608 002, India c Structural Analysis and Testing Group, Vikram Sarabhai Space Centre, Trivandrum 695 022, India b
a r t i c l e
i n f o
Article history: Received 23 October 2009 Accepted 16 January 2010 Available online 22 January 2010
a b s t r a c t This paper examines the tensile fracture behavior of 2124Al–10 vol.% SiCp composites by generating the fracture data from the tensile as well as compact tension specimens. The composites were produced through squeeze casting process. For matrix strengthening and improving ductility, the specimens were heat-treated through solutionizing and ageing. The modified inherent flaw model is utilized for fracture strength evaluation. Fracture strength estimations are found to be in good agreement with test results. The modified relationship between the notched strength and the inherent flaw length will be useful for accurate prediction of the notched tensile strength of composite laminates. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Discontinuously reinforced metal matrix composites, especially particulate reinforced aluminium matrix composites, are currently being used in commercial applications [1–5] because of their high elastic modulus, higher strength and lightweight; the ability to economically produce SiC whiskers, platelets and particulates; the ability to use standard shaping methods such as forging, rolling, extrusion, etc. and much less dependence of the engineering properties on directions than with continuous composites. 2124Al–SiC composites are usually made by powder metallurgy route, avoiding the use of liquid metal, which would produce a brittle reaction zone of Al4C3 around the reinforcement. Prasad and Sasidhara [6] have compiled the flow stress data for 2124 aluminium with varying volume fractions of SiC particulate (15 lm) reinforcements in the vacuum hot pressed and extruded at 500 °C for 30 min. The nominal composition of the matrix (2124Al) in wt.% was 4.2 Cu, 0.99 Mg, 0.72 Mn, 0.16 Fe, 0.13 Si, 0.03 Zn, balance aluminium. 2124AA with 10 vol.% SiCp exhibits large grained matrix structure, which restricts the occurrence of superplasticity due to dynamic recrystallization. The material exhibits flow instability in the temperature range 340–420 °C and at strain rates higher than 1 s1. 2124Al30 vol.% SiCp metal matrix composite is difficult to process because of higher SiCp content. Murty et al. [7] have examined
* Corresponding author. Tel.: +91 471 2565831; fax: +91 471 2564181. E-mail addresses: [email protected] (T. Parameshwaranpillai), prlnau_ [email protected] (P.R. Lakshminarayanan), [email protected] (B. Nageswara Rao). 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.01.032
the hot working characteristics of 2124Al–SiCp metal matrix composites. The mechanical properties of the aluminium metal matrix composites (AlMMCs) generally lie somewhere between those of unreinforced aluminium and titanium alloys. However, it is possible to alter the balance of the properties by careful choice of matrix alloy and level of reinforcement. Experimental studies are made on 2124Al–10 vol.% SiCp composites to examine the influence of heat treatment process parameters on the notched and unnotched tensile strength of the material [8]. These composites were produced through squeeze casting process. Cast metal composites are in general extremely brittle and possessing poor mechanical properties. For matrix strengthening and improving ductility, the specimens were heattreated through solutionizing and ageing. Experiments were done at three different solutionizing temperatures, solutionizing time, ageing temperature and ageing time to examine the influence of heat treatment process parameters on the notched and unnotched tensile strength of the material. Compact tension (CT) specimens with varying crack length, crack mouth width and thickness were tested for evaluation of fracture toughness of the material. The scheme of experiments was planned as per the Taguchi’s design of experiments [9,10]. The fractographs of tensile and CT specimens after the test were performed using scanning electron microscope (SEM). Energy dispersive X-ray analysis at different locations of the fractured specimens indicated chemical composition of the inclusions and matrix constituents. Fractographs in general have the features of intergranular decohesion and transgranular cleavage like fracture. High tensile strength and moderate fracture toughness of the material can be achieved for the heat treatment process parameters: solutionizing at 500 °C for 8 h and aging at 200 °C for 12 h.
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Failure predictions of structural components containing crack like defects through fracture mechanics require mechanical and fracture properties of materials. The extraordinary success of fracture mechanics lies in its ability to combine a theoretical framework with experimentally measured critical quantities. Wu et al. [11] have made a brief review on fracture models for assessing the residual strength of notched fibre metal laminates. The existing analytical models can be categorized into three groups: fracture mechanics models [12,13]; stress–fracture criteria [14–16] and progressive damage models [17–19]. The most notable of fracture models are given by Waddoups et al. [12] and Whitney and Nuismer [14]. Waddoups et al. have applied the classical fracture mechanics to predict the static strength of flawed laminated composites. In their model, intense energy regions characterized by a constant through crack length (aci) and extending symmetrically from each side of the holes on specimens was assumed to define the stress intensity factor. Although the fracture data showed reasonable correlation to their model, the characteristic length (aci) is seen to be not constant but varying. Whitney and Nuismer [14] have, on the other hand proposed the point stress and the average stress criteria. In the former, failure was assumed to occur where the unnotched tensile strength of the material coincided with the notched specimen’s stress distribution. The latter criterion assumes failure when the average value of the stress distribution over a fixed distance near a notch reaches the unnotched tensile strength. The main objective of the progressive damage models is to take into account the damage and resulting changes in the stress distribution that occur throughout the loading process. A basic difficulty that arises is the choice of appropriate combinations of failure modes, failure criteria and property degradation laws. Significant progress is still needed in progressive damage models. Fracture mechanics approach, characteristic distance approach and progressive damage approach are being utilized for notched strength evaluation of composite laminates. Each approach has its own advantages and disadvantages and all are complementary to each other. The objective of this paper is to correlate the fracture data on 2124Al–10 vol.% SiCp composite compact tension (CT) specimens using a modification in the inherent flaw model of Waddoups et al. [12]. The details of modifications made in the inherent flaw model for accurate evaluation of fracture strength of flawed configurations are presented below.
Fig. 1. Inherent flaw length (aci) in a center-crack wide tensile panel.
from Eq. (1) using the notched strength (r1 NC ) for r and c + aci for c. Since aci is unknown, one can obtain by equating these two critical stress intensity factors:
K Q1 ¼ r0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi paci ¼ r1 pðc þ aci Þ NC
ð2Þ
The above equation implies that
c þ aci ¼ aci
r0 r1 NC
2 ð3Þ
The stress intensity factor for a tensile specimen having center crack length (2c) and width (W) under the applied stress (r) is [20]:
KI ¼ r
pffiffiffiffiffiffi pcY
ð4Þ
The finite width correction factor (Y) is 2. Modified inherent flaw model The inherent flaw model consists of a sharp notch from which two intense energy regions are modeled as extended-cracks (similar to the Irwin’s plastic zone correction applied in metals) which have a small but finite length ‘‘aci” (see Fig. 1). The length ‘‘aci” is taken to be the characteristic length of an inherent flaw. For the case of the unnotched tensile specimen, the assumption for the inherent flaw represents the case of a center crack tension specimen having crack length ‘‘2aci”. Waddoups et al. [12] have considered the fracture data of notched and unnotched tensile specimens and estimated the inherent flaw size by equating the respective critical stress intensity factors. The stress intensity factor for a wide tensile specimen having center crack is
pffiffiffiffiffiffi K I ¼ r pc
ð1Þ
Here r is the applied stress and c is half the crack length. The critical stress intensity factor (KQ1) for the unnotched tensile specimen can be obtained from Eq. (1) using r = r0 and c = aci. Here r0 is the unnotched tensile strength. From the fracture data of notched tensile specimen, the value of KQ1 can also be obtained
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pc Y ¼ sec W
ð5Þ
The fracture strength (r1 NC ) of the center-crack wide tensile specimen is obtained from the experimental notched strength (rNC) of the finite width tensile specimen by multiplying the correction factor (Y). Using r1 NC , r0 and c, the unknown characteristic length, aci is found from Eq. (3) as:
( aci ¼ c
r0 r1 NC
)1
2 1
ð6Þ
After determining the characteristic length (aci), the fracture strength (r1 NC ) can be obtained directly from Eq. (3) specifying the crack length (2c). Fracture strength (rNC) of the finite width plate can be obtained by dividing the determined r1 NC with the correction factor, Y. It is noted from the fracture data on different materials that the fracture strength decreases with increase in the crack size. Eq. (6) indicates that the characteristic length (aci) is not a material constant. It increases with increase in the crack size. This calls for a modification in the inherent flaw model.
T. Parameshwaranpillai et al. / Materials and Design 31 (2010) 2987–2993
From the above observations one can write a relation between aci and r1 NC in the non-dimensional form as:
2.2. Compact tension (CT) specimen [20,22]
r1 2 aci ¼ a 1 m NC
c P ; K I ¼ pffiffiffiffiffiffi Y B W W
r0
ð7Þ
The parameters a and m in Eq. (7) are to1 be determined by a r least square curve fit to the data for aci and rNC0 . For the determination of these parameters, two cracked specimen tests in addition to an unflawed specimen test are required; normally more tests are performed to take scatter in test results into account. It should be noted that m = 0 in Eq. (7) represents the case of constant damage size as per the original inherent flaw model [2]. For the case: m > 1 and r1 NC ¼ r0 ;, Eq. (7) results a < 0. Hence, the variation of the parameter in Eq. (7) can be 0 6 m 6 1. Whenever m is found to be greater than unity, the parameter m has to be truncated to one by suitably modifying the parameter a with the fracture data. If m is found to be less than zero, the parameter m has to be truncated to zero and the average of aci values from the fracture data yields the parameter a. Once a and m in Eq. (7) are known, it is possible to eliminate the characteristic length (aci) from the fracture strength Eq. (3). The resulting non-linear equation for the fracture strength (r1 NC ) is
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffi r0 2 r1 c NC ¼ 1 1 m a r1 r0 NC
ð8Þ
This non-linear fracture strength Eq. (8) is solved using the Newton–Raphson iterative scheme to obtain r1 NC for the specified crack size. The fracture strength (rNC) of the finite width plate is obtained by dividing the determined r1 NC with the correction factor (Y). Expressions for the stress intensity factors to Compact tension (CT) specimen and center-cracked tensile specimen (see Fig. 2) useful in fracture analysis are presented below. 2.1. Center-cracked tensile specimen [20,21]
KI ¼
P pffiffiffiffi c pcY BW W
ð9Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where the finite width correction factor, YðnÞ ¼ secðpnÞ; P is the P load; B is the thickness; W is the width; the applied stress, r ¼ BW and c is half the crack length of the specimen.
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ð10Þ 3
where YðnÞ¼ð2þnÞð1nÞ2 ð0:886þ4:64n13:32n2 þ14:72n3 5:6n4 Þ. P is the load; B is the thickness; W is the width and c is crack length of the CT specimen. It should be noted that the value of KQ for the cracked specimens is obtained by substituting the failure load, Pmax for P in the stress intensity factor equations. The fracture strength of the infinitely large width center-cracked tensile specimen is
K
Q r1 NC ¼ pffiffiffiffiffiffi pc
ð11Þ
3. Results and discussion Compact tension (CT) specimens with varying crack length, crack mouth width and thickness were tested for generation of fracture data of the 2124Al–10 vol.% SiCp composites. The scheme of experiments was planned as per the Taguchi’s design of experiments. Tensile strength and fracture toughness properties of the 2124Al–10 vol.% SiCp composite were generated for different heat-treatment conditions [8]. Nine blanks of 50 50 7.5 mm, 50 50 10 mm, 50 50 12 mm were cut from the extrusion at Annamalai University. The blanks were further machined to final dimensions of the CT specimens as per ASTM E399 standards. The specimens were notched in the L–T orientation. Special care was taken while pre-cracking the specimens with fatigue cracks of controlled lengths. Fracture analysis has been carried out on the fracture data of CT specimens made of of 2124Al–10 vol.% SiCp composites. Using the failure load (Pmax) and the dimensions of the CT specimens in Eq. (10), the stress intensity factor (KQ) is obtained. The fracture strength (r1 NC ) of the infinitely large width specimen is obtained from Eq. (11). Using the values of the unnotched strength (r0) and the fracture strength (r1 NC ) in Eq. (6), the inherent flaw length (aci) is estimated. Table 1 gives the inherent flaw length for the fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for the specified heat treatment process parameters: Solutionizing temperature = 500 °C; Solutionizing time = 12 h; Aging temperature = 200 °C; and aging time = 12 h. The parameters a and m in Eq. (7) are determined r1 NC using the data of aci and r0 from Table 1 through a least square curve fit. For the specified crack length, the non-linear fracture strength Eq. (8) is solved using the Newton–Raphson iterative scheme and obtained r1 NC . The stress intensity factor (KQ) is obtained using Eq. (11) and the failure load (Pmax) of the CT specimen is obtained from the stress intensity Eq. (10) by equating KI = KQ and P = Pmax. Table 2 shows a good comparison of failure load estimates of CT specimens following the modified inherent flaw model with the test results. The parameter m in Eq. (7) for the material is found from the fracture data is zero and hence no variation in the inherent flaw size (aci ¼ a ) with increasing the crack size of the specimen at failure. The relative error (%) between the analysis and test results is computed from
Relative error ð%Þ ¼ 100 ½1 ðAnalysis result=Test resultÞ ð12Þ
Fig. 2. Test specimens for notched tensile strength evaluation of the composites: (a) compact tension (CT) specimen and (b) center-cracked tensile specimen.
Table 3 gives the values of inherent flaw length (aci) for the fracture data on 2124Al–10 vol.% SiCp composites generated from
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Table 1 Fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for the specified heat treatment process parameters (solutionizing temperature = 500 °C; solutionizing time = 12 h; aging temperature = 200 °C and aging time = 12 h). Width (W) = 32 mm; tensile strength (r0) = 282 MPa. Crack Length, c (mm)
Thickness, B (mm)
Crack mouth width (mm)
Failure load, Pmax (kN)
r1 NC (MPa) Eq. (11)
Inherent flaw length, aci (mm) Eq. (6)
10 13.33 16 11 14.66 17.6 12 16 19.2
7.5 10 12 7.5 10 12 7.5 10 12
1.2 1.4 1.6 1.4 1.6 1.2 1.6 1.2 1.4
4.953 5.030 4.990 4.956 4.325 4.580 4.241 3.946 3.697
120.9 104.5 100.1 125.0 96.14 103.1 111.0 95.04 95.75
2.253 2.123 2.309 2.689 1.928 2.716 2.200 2.050 2.502
Table 2 Comparison of analytical and experimental fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for the specified heat treatment process parameters (solutionizing temperature = 500 °C; solutionizing time = 12 h; aging temperature = 200 °C; and aging time = 12 h). Width (W) = 32 mm; tensile strength (r0) = 282 MPa; a = 2.301 mm; m = 0. Crack length, c (mm)
Thickness, B (mm)
10 13.33 16 11 14.66 17.6 12 16 19.2
Crack mouth width (mm)
7.5 10 12 7.5 10 12 7.5 10 12
1.2 1.4 1.6 1.4 1.6 1.2 1.6 1.2 1.4
Failure load, Pmax (kN)
Relative error (%)
Test [8]
Analysis
4.953 5.030 4.990 4.956 4.325 4.580 4.241 3.946 3.697
4.996 5.206 4.982 4.651 4.673 4.259 4.322 4.152 3.562
0.9 3.5 0.2 6.2 8.0 7.0 1.9 5.2 3.7
Table 3 Inherent flaw length (aci) for the fracture data on 2124Al–10 vol.% SiCp composites generated from compact tension (CT) specimens for different heat treatment process parameters as per the orthogonal array L9 (34) of Taguchi. Width (W) = 32 mm; thickness (B) = 7.5 mm; initial crack size (c) = 10 mm. Test runs
1 2 3 4 5 6 7 8 9
Solutionizing
Aging
Temp. (°C)
Time (h)
Temp. (°C)
Time (h)
500 500 500 520 520 520 540 540 540
6 8 10 6 8 10 6 8 10
180 200 220 200 220 180 220 180 200
10 12 14 14 10 12 12 14 10
Tensile strength, r0 (MPa)
Failure load, Pmax (kN)
Inherent flaw length, aci (mm) Eq. (6)
277 335 300 177 222 209 298 314 257
4.294 3.338 3.169 3.784 4.065 3.812 5.800 4.309 5.001
1.672 0.629 0.712 3.744 2.497 2.473 2.916 1.264 2.914
compact tension (CT) specimens for different heat treatment process parameters as per the orthogonal array L9 (34) of Taguchi. It r1 should be noted from Eq. (3) that rNC0 increases with increasing the inherent flaw size (aci) for the specified crack size. From the data of Table 3, it is possible to generate the fracture strength of the CT specimen for the specified crack size and the heat treatment process parameters. The fracture strength decreases with increasing the crack size. It is very interesting to note from the fracture data of Table 3 that the failure load of the CT specimen is maximum for the specified heat treatment process parameters: Solutionizing temperature = 540 °C; Solutionizing time = 6 h; Aging temperature = 220 °C and aging time = 12 h. These process parameters for the material will provide optimum strength and fracture properties. Fibre reinforced metal laminates (FRMLs) are a new family of aerospace structural materials developed for fatigue critical applications. These materials are laminated sheets of thin and high strength metal layers, viz., aramid/epoxy, cabon/epoxy, glass/ epoxy, etc. Lawcock et al. [18] have presented the tensile fracture strength data from the center cracked configuration of carbon fibre
reinforced metal laminates (CFRML), Aramid fibre reinforced aluminium laminates (ARALL-2) and glass fibre reinforced aluminium laminates (GLARE-2). The fracture data generated by Lawcock et al. [18] are useful to understand the fracture behavior of composite laminates containing central cracks. For the case of central crack configurations, the failure load max is used in Eq. (9) and ob(Pmax) or the fracture strength, rNC ¼ PBW tained the stress intensity factor (KQ). The fracture strength (r1 NC ) of the infinitely large width specimen is obtained from Eq. (11). Using the values of the unnotched strength (r0) and the fracture strength (r1 NC ) in Eq. (6), the inherent flaw length (aci) is estimated. The parameters a and m in Eq. (7) are determined using the data of r1 NC aci and r0 through a least square curve fit. For the specified crack length, the non-linear fracture strength Eq. (8) is solved using the Newton–Raphson iterative scheme and obtained r1 NC . The stress intensity factor (KQ) is obtained using Eq. (11) and the failure load (Pmax) of the center crack specimen is obtained from the stress intensity Eq. (9) by equating KI = KQ max and P = Pmax. The fracture strength, rNC ¼ PBW of the center crack tension specimens is obtained.
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Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [18]
Relative error (%) Analysis
Material: carbon fibre reinforced metal laminates (CFRML) (2/1 lay-up of 2024-T3 + ICI fiberite T300/7714A UD CF/epoxy prepeg) r0 = 883.4 MPa; a = 3.092 mm; m = 0.460 90.02 10.29 422.3 447.1 5.9 90.10 10.03 439.4 450.7 2.6 89.94 19.97 361.5 352.2 2.6 89.94 19.81 370.2 353.3 4.5 90.00 30.08 288.6 291.5 1.0 90.12 29.45 306.1 294.8 3.7 90.00 30.04 304.8 291.7 4.3 90.12 29.41 296.3 295.0 0.4 90.04 29.38 302.8 295.1 2.5 90.14 39.99 240.4 246.2 2.4 90.18 40.21 235.7 245.3 4.0 90.10 40.07 237.5 245.8 3.5 Material: aramid fibre reinforced aluminium laminates (ARALL-2) (2/1 lay-up of 2024-T3 + UD aramid prepeg) r0 = 717 MPa; a = 2.1313 mm; m = 0 100 25 217.1 263 3.0 100 50 163.3 169 3.5 Material: glass fibre reinforced aluminium laminates (GLARE-2) (2/1 lay-up of 2024-T3 + UDR – glass prepeg) r0 = 1230 MPa; a = 2.4048 mm; m = 0.460 99.8 25 478.2 474.8 0.7 100 50 304 306.4 0.8
Table 5 Fracture strength of T300 carbon/epoxy center-cracked tensile specimens. Width, W (mm)
Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [23]
Analysis
Relative error (%)
Material: T300 carbon/941C lay-up: ½ð45=0=90Þ3 =0=90= 45S : r0 = 548 MPa; a=2.7483 mm; m = 0 36.2 6 355.7 48.1 8 334.3 60.2 10 350.7 36.3 10 304.7
372.5 343.7 320.8 311.0
4.7 2.8 8.5 2.1
Material: T300 carbon/ N5208 lay-up: ½0=904S : r0 = 636 MPa; a = 8.12 mm; m = 0.71 25.1 2.8 471.9 25.1 7.8 321.2 50.5 15.2 322.5 76.0 25.2 319.3
472.3 373.9 323.0 279.1
0.1 16.4 0.1 12.6
Material: T300 carbon/N5208 lay-up: ½0= 45=902S : r0 = 494 MPa; a = 4.38 mm; 25.3 2.8 25.4 7.8 50.6 15.2 76.2 25.2
427.1 338.3 282.0 233.8
1.4 6.8 1.7 2.2
Table 4 shows a good comparison of analytical and experimental fracture strength of CFRML, ARALL-2 and GLARE-2. Tables 5 and 6 show the comparison of experimental results of Khatibi et al. [23] and estimated notched strength values of carbon/epoxy and glass fibre/epoxy laminates containing central sharp-notches. The parameter m in Eq. (7) for these materials is found from the fracture data is
m=0 433.2 316.7 287.0 239.1
not zero and hence the inherent flaw size (aci) increases with increasing the crack size of the specimen at failure. The fracture strength is found to decrease with increasing the crack size and analytical results are found to be in good agreement with test results. The validity of the modified inherent flaw model is further examined considering the fracture data [24] on carbon/epoxy and
Table 6 Fracture strength of Scotchply 1002 center-cracked tensile specimens. Width, W (mm)
Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [23]
Analysis
Relative error (%)
Lay-up: ½0= 45=902S : r0 = 320 MPa; a=2.486 mm; m = 0.272 25.0 2.9 25.2 7.7 50.6 14.7 76.0 24.8
226.2 173.8 140.8 108.2
229.9 169.6 137.7 111.5
1.6 2.4 2.2 3.0
Lay-up: ½0=904S : r0 = 422.6 MPa; a = 1.8308 mm; m = 0.363 25.2 2.6 25.0 7.2 50.6 14.9 76.0 25.8
272.6 203.8 170.1 116.1
280.7 201.8 156.5 124.1
3.0 1.0 8.0 6.9
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glass/polyester composites. Table 7 shows a good comparison of analytical and experimental failure loads of CT specimens made of carbon/epoxy. Table 8 shows excellent match of analytical failure loads with test results [24] of center-cracked tensile specimens made of glass/polyester. Boron/aluminium composites are considered for numerous applications, such as jet engine fan blades, landing gears, transmission housing, other aircraft structures, missiles, and aerospace vehicles [25]. Table 9 shows a good comparison of the present fracture analysis results with experimental failure loads [26] of boron/aluminium laminates in symmetric lay-ups of ½45 =02 S containing center notch. The parameter m in Eq. (7) for the materials in Tables 7–9 is found from the fracture data is zero and hence no variation in the inherent flaw size (aci ¼ a ) with increasing the crack size of the specimen at failure. The fracture strength is found to decrease with increasing the crack length. Polymeric composite materials are widely used in automotive applications for reducing structural weight, saving fuel, and improving performance. Accidental impact damage is an important issue in the use of these composite materials as body components. The damages or cracks in the experimental work of Khashaba [27] were represented by notched specimens, which were fabricated from polyester resin reinforced by woven E-glass fibre. The parameter m in Eq. (7) from the fracture data of this material in Table 10 is found to be non-zero and hence variation in the inherent flaw size (aci) can be expected with increasing the crack size of the specimen at failure. Table 10 shows a good comparison of notched tensile strength values of the modified inherent fracture model with Table 7 Comparison of analytical and experimental failure loads of CT specimens made of carbon/epoxy. Width (W) = 80 mm; tensile strength (r0) = 581 MPa; a = 1.583 mm; m = 0. Crack length, c (mm)
28 36 44 52
max (MPa) Fracture strength = PBW
Test [24]
Analysis
22.3 17.4 12.9 8.5
21.8 16.8 12.4 8.4
Test [24]
Analysis
18 27 36
74.9 60.3 52.7
73.8 61.7 52.4
Relative error (%)
1.5 2.2 0.5
Table 9 Comparison of analytical and experimental failure loads of boron/aluminium laminates in symmetric lay-ups of ½45 =02 S containing center notch. Tensile strength (r0) = 848.1 MPa; a = 1.1232 mm; m = 0. Width, W (mm)
25.35 24.56 25.68 25.20 25.83 25.27
Crack length, 2c (mm)
6.68 6.35 6.38 8.00 7.98 7.98
Fracture max strength = PBW (MPa)
Test [26]
Analysis
406.8 420.6 413.7 372.3 358.5 386.1
407.1 415.6 416.2 372.2 373.9 372.8
Crack length, 2c (mm)
Fracture strength, rNC (MPa) Test [27]
Analysis
Relative error (%)
30.9 30.9 30.9 30.9
6 9 12 15
126.6 104.2 87.7 77.2
126.10 104.63 88.98 76.10
0.4 0.4 1.5 1.4
test results [27]. The fracture strength is found to decrease with increasing the crack size.
4. Conclusions Notched tensile strength of 2124Al–10 vol.% SiCp composites is evaluated in this paper considering the fracture data of the material generated from the compact tension (CT) specimens and following the modified inherent flaw model. Fracture strength estimations are found to be in good agreement with test results. The validity of the modified inherent flaw model is examined considering the fracture data of CT specimens as well as center crack tension specimens made of different fibre reinforced metal laminates. For other cracked configurations, one has to find the stress intensity factor solutions and use the inherent flaw model with the modified relationship between the notched strength and the inherent flaw length for accurate prediction of the notched tensile strength of composite laminates.
References
Table 8 Comparison of analytical and experimental failure loads of center-cracked tensile specimens made of glass/polyester. Width (W) = 90 mm; tensile strength (r0) = 135 MPa; a = 4.126 mm; m = 0. max (MPa) Fracture strength = PBW
Width, W (mm)
Relative error (%)
2.5 3.6 4.3 1.8
Crack length, 2c (mm)
Table 10 Comparison of notched tensile strength of GFRP specimens having center cracks (r0 = 291.3 MPa; a=0.8954 mm; m = 0.215).
Relative error (%)
0.1 1.2 0.6 0.0 4.3 3.4
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