True fracture stress

Assuming that 60 % of the craze volume consists of voids, the true stress in the craze fibrils at break can be calculated to be 150 to 300 MPa, which is in the same order of magnitude as the true fracture stress of a bulk PP-sample after necking and strain-hardening... 

Also included in Table I are the true fracture stress (of) calculated from the cross section of the fractured specimen, and the fracture strain (ef). The fracture stress dropped significantly, from 171 MPa for LLDPE to 100 MPa and 35 MPa for 10% and 25% PS, respectively. The fracture stress of the 37.5% PS blend was even lower, 8.5 MPa, but was still higher than the oy value of 5.9 MPa, so the blend deformed in a ductile manner. The blend with 50% PS fractured in a quasi-brittle manner at a stress of 7.0 MPa, which was slightly lower than cry for this composition. The large decrease in Of with increasing PS concentration was consistent with debonded PS particles that were not load-bearing during plastic deformation. 

Figure 6. Schematic of a voided element of the rectangular array for the calculation of true fracture stress (a), and fracture strain (b).

Figure 7. Effect of the parameter ff on the true fracture stress calculated from equation 13. Data for LLDPE-PS blends are included as the open circles.

The stress-strain relationship in the strain-hardening region of the matrix is almost linear. Then, for blends that fracture in the strain-hardening region, the relationship between the true fracture stress (af) and the fracture strain ( f) is given by... 

The ductile-to-quasi-brittle transition occurs because the true fracture stress, as determined by P, decreases with increasing PS more rapidly than the yield stress, determined by P (Figure 9). The critical PS content (Vf>s) at the ductile-to-quasi-brittle transition can be determined from the condition that the true yield stress is equal to the true fracture stress. From equations 8 and 13,... 

Figure 9. Schematic of the effect of PS content on yield stress (atJ) and true fracture stress (ef) to give the ductile-to-quasi-brittle transition.

This depends on what is meant by the fracture stress. The yield stress must be larger than the overall fracture propagation stress, since otherwise the specimen put under stress will undergo yielding rather than fracture. But the yield stress must be smaller than the local (or true ) fracture stress, since otherwise blunting of the crack tip will not occur and pure elastic fracture results. 

A micro-tensile stage used in conjunction with (environmental) scanning electron microscopy offers a promising route to the necessary area characterisation. The stage will record the load while deforming the sample at a set rate, while the microscope is used to locate the likely region of fracture and to monitor whether the sample draws down uniformly or necks locally. After fracture, the sample cross-section at the point of fracture can be measured, and the results used to obtain the nominal or true fracture stress. 

The true fracture stress for PC, taking into account sample cross-... 

---