Plane strain fracture

ASTM E399-90, "Plane Strain Fracture Toughness of Metallic Materials," MnnualBook ofMSTM Standards, ASTM PubHcations, Philadelphia, 1993. 

ASTM D5045-91, "Plane Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials," A.nnualBook ofyiSTM Standards, ASTM Puhhcations, Philadelphia, 1993. 

Substantial work on the appHcation of fracture mechanics techniques to plastics has occurred siace the 1970s (215—222). This is based on earlier work on inorganic glasses, which showed that failure stress is proportional to the square root of the energy required to create the new surfaces as a crack grows and iaversely with the square root of the crack size (223). For the use of linear elastic fracture mechanics ia plastics, certaia assumptioas must be met (224) (/) the material is linearly elastic (2) the flaws within the material are sharp and (J) plane strain conditions apply ia the crack froat regioa. 

Plane Strain Fracture Toughness of Metallic Materials, 1982 Annual Book of ASTM Standards, Part 10, Standard No. E399. 

Note. is the plane strain fracture toughness (see Section 8.9). 

There are a number of restrictions on the test for for it to be a valid measure of plane strain fracture toughness. Firstly, the plastic zone must not extend through the test piece and secondly the thickness of the material must be such that the test is conducted under plane strain conditions. 

Alle the deformation zones contain a finite and equal number of extended chains in their most highly stretched strands. This surprising conformity of the deformation zones may well be the consequence of the imposed plane-strain fracture condition which impedes lateral contraction of the material. However, no quantitative explanation has been presented as yet. A plausible explanation would be to assume that due to the hindered lateral contraction additional tensile stresses are transferred to the most extended strand with each additional chain pulled out of the matrix [112]. 

ASTM-E 399-81 Standard test method Plane-strain fracture toughness of metallic materials... 

ASTM E399 Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials , 1999 Annual Book of ASTM Standard Volume 3.01 Metals-Mechanical Testing Elevated and Low-Temperature Tests Metallography, American Society for Testing and Materials, 1999. 

Ideally, rubber toughening should be accomplished without substantial sacrifices in modulus. For each modified resin, flexural and Young moduli and plane-strain fracture toughness were determined. Examination of various fracture surfaces by scanning electron microscopy showed the effects of modifier composition on the morphology of these multi-phase materials as well as the prominent features of the fracture process. 

Fracture toughness for siloxane-modified as well as ATBN- and CTBN-modified resins was monitored through KIC, plane-strain fracture toughness 44). The Klc values of at least five three-point bend (3PB) specimens of each material were calculated according to Eq. (1)... 

For characterising the fracture behaviour of a bulk material, the interesting K c value is that corresponding to plane strain, K c. Thus, in order to measure K[c, it is necessary to get a large enough sample thickness, B. Actually, one has... 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

According to Eqs. (13.145) and (13.148) the fracture stress in plane strain is a factor 1 /(1-v2) 1 /0.84 1.2 higher than in plane stress. Experimentally, however, the difference is much bigger. The reason for this discrepancy is that Griffith s equations were developed in linear fracture mechanics, which is based on the results of linear elasticity theory where the strains are supposed to be infinitesimal and proportional to the stress. 

In the case of thin sections the measure of toughness is given by plane-stress fracture toughness, Kc and elastic-plastic fracture mechanics (EPFM) are used. It is also necessary to bear in mind that plane-stress fracture toughness Kc is higher than plane-strain fracture toughness Xlc. 

E399, Standard Test Method for Plane-strain Fracture Toughness of Metallic Materials, ASTM, West Conshohoken, PA, 1997. 

---