Glassy polymers as photoplastic materials

Glassy polymers as photoplastic materials

Int. Z mech. ScL Vol. 18. pp. 171-178. P e r g a m o n Pre s s 1976. printed in Great Britain G L A S S Y P O L Y M E R S AS P H O T O P L A S T I ...

1MB Sizes 5 Downloads 195 Views

Int. Z mech. ScL Vol. 18. pp. 171-178.

P e r g a m o n Pre s s 1976.

printed in Great Britain

G L A S S Y P O L Y M E R S AS P H O T O P L A S T I C MATERIALS P. S. THEOCAR1S Department of Theoretical and Applied Mechanics, The National Technical University, Athens (147), Greece (Received 15 August 1975;and in revisedform 20 February 1976) Summary--Polycarbonate of Bisphenol A (PCBA), which is a typical glassy polymer, presents a stress-strain curve in simple tension showing many similarities with load-extension diagrams of metals. This behaviour suggested the possibility of using glassy polymers and especially PCBA as model materials for studying plastic deformations in metals. However, significant differences between polymers and metals exist with regard to their yield behaviour. Considerable evidence is presented in this paper, which shows that there are qualitative and quantitative differences between the mechanisms of plastic deformation in metals and in glassy polymers. Therefore, an eventual use of such polymers as models for studying plastic behaviour may be made only to obtain qualitative results.

1. INTRODUCTION IN RECENT years many attempts have been made for the experimental investigation of plastic states of stress by using model materials in combination with the optical method of photoelasticity. The problems involving plastic deformations may be distinguished between the problems with large deformations and those incorporating constrained yield phenomena. For the experimental solution of these two classes of problems by using polarized light two different approaches under the general name of photoplasticity have been mainly developed. The one approach "the so-called photoplasticity in the narrow sense of the term" tries to evaluate the distribution of plastic stresses and strains in prototypes, which mainly are metallic plates, by using models made of polymers exhibiting mechanical properties similar to metals. The other approach studies plastic strain distributions on the surfaces of metals by making photoelastic measurements of the elastic strains in birefringent coatings cemented on the one lateral face of the metallic specimens. Although this method evaluates only surface strains of metals, it presents many advantages for the solution of plasticity problems. A comprehensive survey of the above methods with many practical applications may be found in the book by Javornicky} where among others all the experimental contributions concerning plasticity are reviewed. In the following we will refer only to the first approach, that the so-called photoplasticity by pointing out the potentialities and the drawbacks of the method.

Extensive tests made by Frocht and his coworkers ~ used celluloids (cellulose nitrates) as photoplastic materials. This group of studies related uniquely the isochromatic fringes to the principal stress difference and proved that the principal stress axes of the specimen coincides always with principal birefringence axes. For the same type of material (celluloid) another group of papers by M6nch and co-workers 7-~2 in Germany, indicated that isochromatics are related to strain. These papers did not study the orientation of the principal stress-, strain- and birefringence-axes. This group of studies used the anomalous birefringence dispersion threshold, appearing with impending plastic deformation in the specimen, for determining the plastically deformed zones and evaluating plastic strains. Another type of material proposed for applications of photoplasticity was polyethylene. 13-~5This material presents a linear relationship between isochromatics and shear strains. However, a drawback of this particular type of polymer is that it presents a Poisson's ratio at plastic deformation of the order of 0.2, which is far away from its customary value of 0.5 for metals in the plastic region. Polystyrene ~6and Nylon 17have been also proposed as presenting sharp yield points in uniaxial tension and a linear relationship between isochromatics and axial strains, but both these materials present strong viscoelastic behaviour. Another attempt was to use silver chloride, t8'~9 which is a crystalline material, and it presents a linear relationship between isochromatics and axial stresses in simple

171

P. S. THEOCARIS

172

t e n s i o n . All t h e s e a t t e m p t s did n o t s u c c e e d in e s t a b l i s h i n g a g e n e r a l a n d unified m e t h o d f o r studying plastic b e h a v i o u r of metals b e c a u s e , a m o n g o t h e r s , of their i n c a p a c i t y to simulate t h e p r o c e s s of plastic d e f o r m a t i o n in crystalline bodies. R e c e n t l y it h a s b e e n s u g g e s t e d b y m a n y i n v e s t i g a t o r s 2°-23 t h a t p o l y c a r b o n a t e of b i s p h e n o l A ( P C B A , L e x a n ) is a suitable material, since it p r e s e n t s small v i s c o e l a s t i c p h e n o m e n a at a m b i e n t t e m p e r a t u r e a n d satisfies the f o l l o w i n g b a s i c req u i r e m e n t s for a s a t i s f a c t o r y e l a s t i c - p l a s t i c analysis: (i) A similarity in s t r e s s - s t r a i n c u r v e s for prototype and model materials (ii) A s a t i s f a c t o r y r e s e m b l a n c e in t h e yield l o c u s for multiaxial loading b e t w e e n the p r o t o t y p e a n d the m o d e l m a t e r i a l s (iii) A c o i n c i d e n c e b e t w e e n t h e lateral c o n t r a c tion ratio ( P o i s s o n ' s ratio) v e r s u s s t r a i n or s t r e s s c u r v e s b e t w e e n t h e m a t e r i a l s of m o d e l s a n d t h e prototype, and (iv) A v i s c o e l a s t i c b e h a v i o u r of t h e m o d e l m a t e r ial o b e y i n g t h e b a s i c r e q u i r e m e n t s (a) of linearity b e t w e e n b i r e f r i n g e n c e , stress a n d s t r a i n a n d (b) of c o i n c i d e n c e of t h e limits of linearity of t h e s e q u a n tities in the r e s p e c t i v e s t r e s s - s t r a i n - b i r e f r i n g e n c e curves. A l t h o u g h p r e v i o u s i n v e s t i g a t o r s 24 w e r e satisfied with resemblances found between prototype materials, w h i c h p r e s u m a b l y m u s t b e m e t a l s u s e d in e n g i n e e r i n g applications, a n d P o l y c a r b o n a t e , especially for t h e first t w o r e q u i r e m e n t s , t h e s a t i s f a c t i o n of t h e last t w o r e q u i r e m e n t s , w h i c h is equally i m p o r t a n t as t h e p r e v i o u s o n e s , e i t h e r was neglected or not fully e n c o u n t e r e d . In this p a p e r w e shall discuss, o n e b y one, t h e d e g r e e of s a t i s f a c t i o n of e a c h of t h e s e r e q u i r e m e n t s in o r d e r to s h o w t h a t P C B A is n o t suitable to yield a c c u r a t e q u a n t i t a t i v e results w h e n it is u s e d as a model m a t e r i a l to s i m u l a t e plastic b e h a v i o u r in metals. 2. VISCOELASTIC BEHAVIOUR OF P C B A AT AMBIENT TEMPERATURE

It has been suggested by Bril123that PCBA, which is an uncrosslinked polymer (glassy), presents time effects, which are small for initial stress levels up to 6000 psi (4.2×107Nm-2). However moir6 accurate measurements 2~.26 revealed that time effects start to become not negligible for tensile stresses above (2.0-3-0) × 107 Nm -2. Thus, although PCBA at room temperature is below its glass transition temperature Tg, there is a perceptible viscoelastic behaviour of the material, that is its mechanical and optical characteristic quantities are functions of time, temperature or frequency. Therefore, while the general adoption of the simplifying assumption that the rate averaged values for all mechanical and optical characteristic functions may satisfy roughly the particular conditions

of each problem, they must be used with great care, especially in cases of extrapolations, where the intrinsic properties of the material are masked and cease to correspond to these average values. This is true even for the rheo-optically simple materials, where they present in their glassy region a small but perceptible, variation of their mechanical and optical properties with time, temperature, frequency and increase of load. Besides the generally expected viscoelastic behaviour for any rheo-optically simple polymer, polycarbonate presents a very strong non-linearity as the external load is increased. 2~-2~ This non-linearity of the mechanical and optical characteristic properties of PCBA is presented in Figs. 1 and 2, which give the variation of stress ~r, relaxation modulus E and the strain and stress-optical coefficients C, (t) and (c~ - c2) vs strain ~ for values of strain up to E = 6%. This value of strain corresponds to the initiation of necking in the PCBA tension specimen. All these figures correspond to a temperature T equal to T = 20°C and a total time interval equal to t = 100 sec. Fig. 1 was extracted from ref. (25) and (26), while Fig. 2 from ref. (30). it is clear from these figures that the limits of nonlinearity for the same material are different for the mechanical and the stress-optical properties. Indeed, it is shown from Figs. 1 and 2 that, while mechanical linearity of the material is extended up to a strain E = 1.0 × 10 -2 the optical linearity is extended longer up to a strain of = 2-0 × 10-2. It can be deduced from these two figures that the limits of linearity of birefringence and strain are not coincident. Therefore in the interval between the two limits, while the one quantity will increase non-linearly, the other will still vary linearly, thus, creating an obvious regional anomaly in the correlation of these two quantities. Since our interferometric measurements 2s'26'3'were executed with very stringent conditions (strictly isothermal conditions and isochronous measurements after quasiinstantaneous loading) and our experimental method is much more sensitive than classical photoelasticity, 3' the linearity in the variation of birefringence versus stress or strain up to a strain of 6%, claimed by various researchers (for instance ref. 23), is only a crude approximation. Similarly, it is a crude approximation that mechanical and optical creep are negligible below 6000 psi (4-2 × 107 Nm 2). Thus, it is concluded that viscoelastic effects in PCBA are non-negligible even in the initial part of the stressstrain curve of the material, while nonlinear effects in the mechanical -nd stress-optical properties of the material are introdu. ¢d at different stress or strain levels as the deformation of the specimen is developed. Therefore the requirement of linearity between birefringence, stress and strain for the photoplastic model material and the simultaneous attainment of the linearity limits for these quantities are not strictly satisfied by PCBA. These requirements are necessary for an exact experimental study of the evolution of plastic enclaves in various materials in the early stages of incipient plastic deformation. 3. THE ISOTHERMAL STRESS--STRAIN CURVE IN TENSION With a constant rate of elongation and under controlled constant humidity and temperature below the glasstransition temperature T~ for the polymer a tension specimen made of PCBA stretches uniformly up to a strain equal to 6%.

Glassy polymers as photoplastic materials

173

= f(c)

!

T 'E z

I

z

...

,01 "7 Z ca v

E

c2) = ~o(E) x

0 x

U I

0

3

i 4

(%) FIG. 1. Initial part of the stress-strain curve in tension up to necking and variation of the stress optical coefficient (c, - cO and the relaxation modulus E for polycarbonate at a cross-head speed equal to 1 cm/min at ambient temperature.

I

3.0

o

E(t)-points



CE(t)-points t = 102 sec.

P

0

"~ 2.0

"0~=

td 0

f(E)

'E Z v

q~

o 1.0 x

LU i

0

1

i

2

3 e(%)

J

4

5

6

FIG. 2. Variation of the strain-optical coefficient C, and the relaxation modulus E vs engineering strain e for polycarbonate at ambient temperature extracted from ref. (30). The initial part of the load-extension curve for PCBA at room temperature and at a cross-head speed of 1 cm/min up to a strain equal to • = 6% is shown in Fig. 1. This curve presents a very restricted initial linear region for strains up to 1% and then a non-linear part up to a strain of the order of 6%. At this limit of uniform straining a constriction or neck initiates in the specimen accompanied by a slight drop of the applied load. For further loading, necking is progressively spread all over the length of the specimen. Figs. 3(a) and (b) show the transverse

and longitudinal moir6 patterns for two steps of the evolution of necking, while Fig. 3(c) shows a transverse moir6 pattern when the necking is extended all over the tensile specimen. It is clear from the transverse moir6 patterns, from the deformed scribed lines in the neck, as well as from the fracture markings of the moir6 coating membrane, that, although in some central areas of necking there is a uniform plastic strain, in the rest of the necking, which is "[he larger part of it, strain is not uniformly distributed. Furthermore, the thickness and the width of the specimen in the necking are randomly varying and therefore the assumption for a uniform tensile stress applied in the specimen is, again, a crude approximation. The overall elongation of the specimen during the expansion of necking is of the order of 80% of the initial length of the specimen. After the necked region was expanded all over, the material strain-hardens continuously up to fracture, which occurs at a strain approximately equal to e = 100%. The region of strain-hardening of the material extends only a few percent, in strain and the rise of stress is rather limited. This means that the region of a true and uniform plastic deformation of the specimen is rather restricted, while the region of non-uniform strain distribution, due to the evolution of necking, is largely extended. This contrasts with metals, illustrated by mild steel, where only the L~iders strain instability appears as a non-uniform strain perturbation of small extent not exceeding 2-3%, while the true plastic behaviour covers an overall strain of the order of 20%. Furthermore, while in most cases with glassy polymers there is a clear evidence~2for the existence of an intrinsic yield drop, that is a fall in true stress, there is a significant difference between polymers and many metals in connection with yield behaviour. Indeed, in all polymers two maxima are observed on the true stress-true strain curve, which are associated with necking of the specimen and

174

P . S . THEOCARIS !

I

%

'E z2

-E Nu

(2) m

'E

'Sp

z

(1) DIN St.37 (2) PCBA

"~

b

.

.

.

.

.

.

3

Z

i

20

/.,0

60

L

0

80

100

(1_

E (,/,) FIG. 4. Stress-strain curves in tension for specimens made of mild steel under the commercial designation DIN St. 37 and polycarbonate. the strain hardening of the material after the expansion of neck all over the specimen. The first maximum in the true stress-strain curve of the material is of major importance, since the existence of the second maximum, which occurs after the neck is expanded all over the specimen, depends mainly on the rate of loading, the size and shape of the specimen and the conditions of loading. For this reason many authors consider only one real maximum in the true extension curve of the glassy polymers.3~On the contrary, in many metals only one maximum is often observed on this curve. This maximum represents a fall in true stress, which is of intrinsic character and corresponds to a sudden increase of the amount of plasticity resulting in a relaxation of stress. A second maximum is observed deeply in the plastic area of deformation in the conventional stress-strain curve of the material, where the material strain-hardens to different amounts but uniformly all over, at the point where necking is initiated. This maximum appears .when the strain-hardening of the metal is exceeded by the geometric softening due to the reduction in the cross section of the specimen and disappears when the true stress--strain curve of the metal is plotted, while the first maximum persists to exist in this curve.

Andrews & Whitney3~ and Brown & Ward ~2 have shown that the first maximum in glassy polymers combines the effect of geometric changes and an intrinsic load drop and cannot be attributed only to geometric changes. It is important also to note that every element of the band of the material of the polymer, which enters in the necking region, does not follow the same true stress-strain curve, since the stress for initiation of necking is always greater than the stress for propagation of the neck. Fig. 4 presents the stress-strain curves in tension for a mild steel specimen, as well as for a PCBA specimen. Both curves are traced under the same scale of strains, since these are the comparable quantities for studying the plastic behaviour of the two materials. Although there are similarities between the stress-strain curves of metals showing a Ltiders' instability region and of glassy polymers showing a progressive neck, there are also important differences in the plastic behaviour of the two groups of materials, which do not allow the use of the one type of material as model to study the plastic behaviour of the other group. Indeed, the elastic range of the metal may be

simulated with the linear and non-linear behaviour of the plastic of the model. This may be acceptable, but with the limitations already discussed in the previous chapter. The yield point of the metal may correspond to the initiation of necking in the polymer. Up to this point the analogy between the two phenomena is legitimate. But beyond the yield point most metals (mild steels) present a limited region of nonuniform plastic straining, where Liiders bands are nucleated and propagated all over the specimen, whereas other metals (aluminum alloys) do not present any such instability. However, even in metals with a Liiders strain instability this region does not exceed in all cases a strain of the order of 3-6% (point Sm of curve (1) of Fig. 4). Beyond this limit the metal deforms plastically in a uniform manner with different amounts of strain hardening, until necking appears. The analogous region in the PCBA is the region (N, S~ ) in curve (2) (drawn in figure by dashed line), where the necking is propagating all over the specimen. This region cannot be associated with the uniform plastic behaviour of the metal (region (Sin - F , ) in curve (1)) for the main reason that, although the overall stress in the plastic specimen remains constant, the distribution of strain is highly non-uniform containing plastic zones with rather non-uniform strains and elastic zones outside the neck. Furthermore, the stress levels at different points of the specimen vary, depending on the irregular variation of thickness and width of the specimen in the plastic zone, as well as on the different amounts of elastic relaxation outside the neck. This strongly non-uniform quasi-plastic deformation of the specimen extends up to an overall strain of the order of 80%. Finally, the short strain-hardening region of the glassy polymer (curve S ~ - F , ) with uniformly distributed strains all over the specimen is covering only a few percent of the total deformation of the specimen, in contrast of the strain-hardening region of the metal, which covers the larger part of the corresponding stress-strain curve. It is seif-evident that it is not legitimate to simulate the Liiders' region (region (P. -Sm ) of curve 1 of Fig. 4) of the metal with the region of propagation of neck all over the polycarbonate specimen (region (N~ - Sp ) of curve 2 of Fig. 4) since (i) the Liiders' region does not occur in all metals (ii) it covers only a very small interval in the

FIG. 3. Transverse (a, c) and longitudinal (b) moir6 patterns of a tension specimen made of polycarbonate after initiation of necking. Cases a and b correspond to two intermediate steps of evolution of necking, while case c is when the necking is extended all over the specimen.

f.p. 174