Yield Crazing and Fracture

Presented by: Omid NirooFar, Arash Nekooei ,Aslan Baharloo

Table of ContentA.Concepts

Brittle And Ductile Fracture

Introduction to Shear Yield Introduction to Crazing

B. Shear Yield Basic Concepts Mechanical tests Yield Criteria Viscoelastic Nature of

Yield Behavior: The Eyring

C. Crazing Morphology & Types of Crazes Crazing Criteria Crazing and polymer structure Crazing & Environmental

Agents Stress Strain Behaviors of

Craze

D. Fracture in Polymers Brittle-Ductile Transition Fracture Mechanics Impact Strength Impact Resistance: polymers

Modified with Rubbers

3

A: Concepts

A. Brittle Fracture: cracks spread very rapidly, with little deformation. cracks are more unstable and crack propagation will continue

without an increase in the applied stress.

B. Ductile Fracture : has extensive plastic deformation. The process proceeds relatively slow . The crack resists any further extension unless there is an

increase in the applied stress

Imposed stress Crack FormationPropagation

4

SemiCrystalline polymers&

Amorphous PolymersAtSemiCrystalline polymersAt

Ductile Fractureone piece

large deformationWarning before fracture

Brittle Fracturemany pieces

small deformationsNO Warning

6

The most important mechanisms that can lead to plastic deformation in polymers are Shear yielding

and Crazing

Yielding is involved in ductile failure of polymers if the

strain applies on Bulk of Specimen and if the strain

applies on segments, leads to

local crazing which precedes brittle fracture.

yield in polymers depends on temperature and strain rate

and is also affected by pressure, and the stress-strain

curves are dependent on the type of test: tension,

bending, or compression.

7

B: Shear Yield

Shear Yield Basic Concepts

Mechanical tests

Yield Criteria

Viscoelastic Nature of Yield Behavior: The Eyring

8

Basic Concepts

9

10

Mechanical tests: Uniaxial tension Deformation

As The true Stress:

As The nominal Stress:

Strain: True Uniaxial Strain:

11

Mechanical tests: Uniaxial compressionPros. : The Stress is compressive No possibility of Brittle Fracture Yield Stress is made under conditions of

Stable deformation (such as formation of neck)

Cons. : Diameter/Height ratio of the sample Area of Specimen increases

Mechanical tests: Plane Strain

compressionPros. : Area of Specimen remains constant

12

Mechanical tests: Simple Shear

Shear Stress:

Shear Strain:

13

Yield Criteria

yield occurs when the maximum shear stress reaches a critical value.

The Tresca yield Criterion:

If:

Then:

In simple tensile test So

Tresca Yield Criterion was Developed for Metals But Most metals obey Von Mises Criterion Better

14

Von Mises Criterion:

conditions for shear yielding in isotropic polymers are best summarized by theVon Mises Criterion

yield occurs when the elastic shear strain energy density in the stressed material reaches a critical value in this case of simple tension

Experimental data show that neither the Tresca nor the von criterion adequately describes the shear yielding behavior in polymers.

15

Pressure-dependent Yield Behavior:

Hydrostatic pressure on polymers

Yield Strength of Polymer

Van Der Waals Solids

So:

Strain rate dependent yield at zero Pressure

Material Constant

16

Geometric representation of the modified Von Mises and Tresca Criteria

Tresca CriteriaVon Mises Criteria

17

Viscoelastic Nature of Yield Behavior

a function of strain at 25°Ca function of temperature at = 0.083

18

The Eyring Model The model assumes that when a segment of a macromolecule has to move to an adjacent site it must pass over an energy barrier represented as ∆ * In the absence of stress, the 𝑬segments of the polymer jump over the barrier infrequently, and they do so in random directions. The frequency with which the segments jump the barrier is represented by the Arrhenius equation

𝟏↔𝟐

Stress

19

𝑣−1 ≪𝑣1=0

20

yielding is described as viscous flow in which the activation energy barrier E* for load shear displacements of polymer segments is decreased by the applied stress . The imposed strain rate, can be considered proportional to the net rate flow, and can be considered the maximum shear stress; then = /2,o being the tensile yield stress. Consequently:

Which can be arranged as:

21

C: Crazing

Crazing Morphology & Types of Crazes

Crazing Criteria

Crazing and polymer structure

Crazing & Environmental Agents

Stress Strain Behaviors of Craze

22

Crazing is a characteristic of thermoplastic polymers and plays a major role in their fracture, particularly in cases of brittle fracture .fracture in polymers cannot be explained without mentioning crazing.Crazes are observed in high molecular weight glassy polymers other than thermosets.Crazes are found in the interior of the material and on its surface as well as at the tips of cracks.

23

Dependence of Crazing stress on temperature at Different Strain rate of polystyrene. Strain rates: (●) 0.00067, () 0.0267, (▲) 0.267

Relationship between yield stress and

crazing stress with temperature, for

polystyrene

24

Morphology & Types of Crazes

Crazes, in all cases, consist of elongated cavities and fibrils oriented in the main

direction of the stress Crazes in amorphous polymers can be classified into three

types depending on where crazing occurs:

1. surface crazes2. crazes at a crack tip3. internal crazes

25fibrillar bridges microvoids crack

aligned chains

Crazing Criteria: IntroductionCrazing is a cavitation process and take place with and increase in volume.It is favored by the presence of triaxial tensile stresses and can be inhabited by applying a hydrostatic pressure. The cavitation involved in the crazing permits the material to achieve plastic strain faster. the presence of marked cracks or defects in bulky samples will favor the initiation of crazing. These defects are points of high concentration of stresses and can cause the formation of initial micro voids.

26

Crazing Criteria: Sternstein-Ongchin Criterion

Sternstein and Ongchin considered that if cavitation occurs in crazes the criterion

for crazing initiation should include the dilative stress component

The Sternstein-Ongchin criterion is expressed in terms of the stress:

Stress required to orient the fibrils

In plane Stress: and So

27

Envelopes for the initiation of crazing and shear yielding in PMMA

28

Crazing and polymer structure

The effect of polymer structure on crazing has been explained in terms

of molecular entanglements.

For a craze to be stable, there must be molecular entanglements

For polymer chains of molecular weight high

enough that they can be considered Gaussian coils,

the maximum extent that the chain between

entanglements can be stretched : length between entanglements

The Maximum Extent that the chain between entanglements can be stretched

The Average distance Between entanglements

29

Experimental extension ratio of Crazes, λ In homo- and copolymers versus the theoretical maximum extension ratio

λ

30

Molecular weight

dependence of fracture

stress and

(●) Crazing stress for

polystyrene

For , crazing occurs and the failure starts from crazes, the fracture

stress increasing as the molecular weight increases

31

Crazing and Environmental Agents

In general, environmental agents reduce the stress or strain required to initiate crazing.

In order to evaluate the acceleration of

crazing by action of a solvent, the

interaction between the polymer and the

solvent can be quantified by means of the

solubility parameter, , defined as the

cohesive energy density where is the

vaporization enthalpy and V is the molar

volume.

32

Relationship between

the critical strain of a

polymer and the

solvent solubility

parameter

33

Stress Strain Behaviors of Craze

A craze containing even 50% micro cavities can still withstand loads because fibrils,

which are oriented in the direction of the load, can bear stress.

It can be seen that the modulus of the crazed polymer is similar to that of the bulk polymer, but yielding of the craze occurs at a relatively low stress and is followed by strain hardening. From the loading and unloading curves, larger hysteresis loops are obtained for the crazed polymer than for the bulk polymer.

34

D: Fracture in polymers

Fracture in Polymers Brittle-Ductile Transition

Fracture Mechanics

Impact Strength

Impact Resistance: polymers Modified with

Rubbers

Fracture is the creation of two new

surfaces in a material by the

application of external forces.

35

Brittle-Ductile Transition

As Figure shows how a typical amorphous thermoplastic, changes in

behavior from brittle to ductile with a simple increase in temperature.

If crazing dominates, the

behavior of the polymer is brittle,

but if shear yielding occurs, the

polymer is ductile.

36

as is illustrated schematically in Figure the stress required to cause brittle fracture, and the yield stress, decrease with increasing temperature, but the variation of is more marked At temperatures below TB, the yield stress exceeds the brittle fracture strength and the process that takes place is the one requiring the lowest stress, i.e., brittle fracture.

𝑇 𝐵 At T > the situation is reversed

and

, leading to yield and ductile failure.

The temperature is called the

brittle-ductile transition

temperature.

37

the strain rate also influences . It has been found that while brittle 𝑇𝐵fracture is hardly affected, the yield stress changes significantly with

the strain rate. As shown in Figure, when the strain rate increases, 𝜎𝑦increases. Therefore the brittle-ductile transition temperature

increases, as does the strain rate.Effect of the strain rate on

Low rate of strain ( )

high rate of strain (

)

38

Fracture Mechanics: Griffith Theory of fracture

surface free energy per unit area of surface

Associated increment of surface

Work done= elastic energy + surface energy

The work done to propagate a unit area of crack

39

Due to first law of thermodynamic:

U = Ue +UsU= Total energy of the systemUe = elastic strain energyUs = energy in creating new crack surface area

Crack Growth rateStrain

Temperature

40

and the total energy change is:work done when the crack propagates

decrease in elastic energy

limit from which the crack ceases to be

stable

41

Irwin gave an alternative formulation to fracture by considering the distribution or field of stresses around a crack in an elastic material. He proposed that such a distribution could be expressed as a function of a parameter K, known as the stress intensity factor, and he established that the fracture would occur when K

exceeds a critical value Kc characteristic of each material.

Fracture Mechanics: Irwin’s Model

42

For an infinite sheet with a central crack of length 2c subjected to a uniform stress it was shown by Irwin that:

He postulated that, when reaches the fracture stress , has a critical value given by:

The fracture toughness of the material then can be defined by the value of, termed the critical stress intensity factor, which defines the stress field at fracture.

In the case of thin lamina:

for thick lamina:

Crack propagationStable Crack

43

44

Owing to the amplification of stresses at the crack tip, the value of the yield stress can be exceeded in that zone, leading to localized plastic strain.

Zone of plastic strain at the tip of a crack

45

Impact strength tests determine the capability of a material to maintain its structural integrity and to absorb energy in a Sudden impact.

Impact Strength

IZOD CHARPY

46

47

Impact Resistance: polymers Modified

with RubbersClassy polymers, PMMA and PS, are suitable for many applications, but they are brittle when subjected to impact loads.

To solve this problem, impact-resistant polymers have been developedI. blending an immiscible elastomer

II. synthesis of block copolymers

48

E: Complementary Information

Differences in Crazing Mechanism And Shear Yielding Mechanism (Refers to Slide 6)

How to Determine Experimentally (refers to Slide 29)

How dose Crack happens in polymer/Solvent systems with Near Solubility Parameter (refers to Slide 32)

49

Differences in Crazing Mechanism And Shear Yielding Mechanism

Failure of Glassy polymers involves two mechanisms: 1. Shearing is a plastic deformation mechanism characterized by a

continuum flow, without the creation of an internal surface. From the viewpoint of energy dissipation and toughness considerations, shearing is far more effective than crazing because the entire volume of the plastically deforming material is participating in the energy dissipation.

2. Crazes are initiated when the external stretch causes a microscopic void to open up at a stress concentration created by a pre-created notch, a heterogeneity in the molecular network or a foreign particle. It is clear that the probability of such microscopic voids to occur is dependent on the local stress situation.

Reference: Kramer EJ, Berger LL, 1990, Adv Polym Sci 91-92:1

50

How to Determine Experimentally

Transmission electron micrograph of a craze in a 680-340-680 triblock copolymer. Measured average extension

ratioin a "parallel" area: = 4.3 and in a "perpendicular“ area: "

perpend. = 5.0.

Transmission electron micrographs of a craze in a 340-340-340 triblock copolymer strained to = 0.05. No staininghas been used. Note how the areas where the lamellae are

oriented perpendicular and parallel to the fibril direction canbe clearly distinguished.

Experiments have shown that a craze grows in width by pulling fresh material into the craze fibrils from a narrow (10-30 nm) fluid-like active zone at a basically constant extension ratio This extension ratio has been measured by a quantitative transmission electron microscopy TEM technique.

Reference: C. Creton, E. J. Kramer and G. Hadziioannou, Craze fibril extension ratio measurements in glassy block copolymers, Colloid Polym Sci 270:399-404 (1992)

51

How dose Crack happens in polymer/Solvent systems with Near Solubility Parameter

Reference: A.L. Volynskii and N.F. Bakeev Eds. Solvent Crazing of Polymers 1995

Fracture Mechanics role in crazing: G = the work of craze (crack) growth in

the materials

surface area of growing craze

Andrews and Bevan were the first to apply the methods of fracture mechanics for analyzing craze growth in PMMA in the presence of a series of aliphatic alcohols, aqueous alcohol solutions, and CCI4.The value of G was found to depend on the solubility parameter of liquid environment. Minimal work for craze nucleation is associated with those liquids, solubility parameters of which are close to that of polymer.

52

Analysis of craze growth from the notch tip in the PMMA samples in the presence of liquid environments was carried out by Williams, Marshall, and coworkers. They showed the existence of a certain correlation between critical stress for solvent crazing and polymer solubility parameter.

Reference: A.L. Volynskii and N.F. Bakeev Eds. Solvent Crazing of Polymers 1995

The minimal was observed in those liquids, whose is close to that of polymer. Evidently, in this case, liquid was assumed to plasticize the stressed region at the craze tip, and polymer resistance to deformation decreases.

Crack May Happen BeforeDissolution

F: Problems1. A wide sheet of polycarbonate that contains a central sharp crack

of length 2a = 20 mm fractures at a stress of 13.5 MPa.(a)Calculate for polycarbonate(b) Calculate the fracture stress of a wide sheet containing a crack of length 40 mm.(c) Will a crack of 10,mm in a similar sheet fracture under a stress of 10 MPa.

2. The stress-strain curve for a material can be represented by means of the function = 12, where , represents the true tension stress in and is strain. Calculate the value of the strain at the necking point and the value of the yield stress,

3. Explain Sternstein-Ongchin Crazing Criterion.

4. What are the effective parameters on deformation mechanisms (Shear yielding & Crazing) when do they dominate each other.

5. Explain and tell what is the effect of strain rate and temperature on it.in case of ignoring , Example a major consequence in application.

THANKS For Your Attention