True fracture stress calculation

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.

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).

The fracture strength of a material is the normal stress at the beginning of fracture. It is calculated from the load at the beginning of fracture during a tension test and the original cross-sectional area of the specimen. Fracture stress is the true, normal stress on the minimum cross-sectional area at the beginning of fracture. 

The mechanical properties of elastic materials are characterized by ultimate fracture stress (strength), fracture strain, and Young s modulus (the ratio of stress to strain). The mechanical response of ductile materials is non-linear and their properties are additionally characterized by yield stress and draw stress (also called lower yield stress) if a polymer yields with necking. The cross-sectional area of a specimen reduces during yielding, and stress is calculated as a ratio of an applied force to the initial cross-section (engineering stress) or to the current cross-section of the specimen (true stress). Here engineering stresses are used. 

Also shown in Fig. 1.26 is the true fracture strength which is the true stress at final fracture, and is calculated by Eq. (1.16) ... 

Prior investigations into the behavior of notched specimens of materials have used the approach of recording a load and displacement and then photographing the fracture surface immediately after the test to obtain the ultimate axial true stress [26]. This method is acceptable in metals, but UHMWPE shows substantial strain relaxation upon fracture (Figure 31.3), which leads to inaccuracies in the calculated true ultimate stress. Also, this method does not provide information as to what is the deformation behavior of the notch during the test itself. Additionally, any method that uses a form of measurement that involves contacting extensometry risks premature fracture of a UHMWPE specimen due to the creation of a stress riser at the point of contact of the extensometer. Therefore, we developed a video-based system that could capture the stress-strain behavior throughout the duration of the test and avoid specimen contact [3]. 

Plastic flow in crystals occurs by dislocations moving on slip planes that slide over one another. Most experiments with single crystals to determine the CRSS are performed with tensile specimens. The shear stress on the active slip plane is computed by resolving the tensile stress onto the active slip plane. With polycrystalline tensile specimens, plastic flow still occurs on slip planes in the individual grains and these are grouped into wide shear bands that traverse the specimen at 45° from the tensile axis. The shear stress is usually calculated approximately for the whole specimen by dividing the tensile stress in half. Failure of a ductile tensile specimen usually occurs by initiation of a shear crack that is followed by a mode I crack that is normal to the tensile axis. Sudden flnal failure occurs when the true tensile stress exceeds the mode I fracture stress. 

A typical tme stress-true strain curve of Type (A) specimens is shown in Fig. 2. The tme strain is calculated from the displacement of cross-head. As can be seen, the fracture of the specimens occurs at a strain of about 0.5. Relation between true stress, a, and true strain, , in uniformly deformed Type (A) specimen is given by the following Ludwik law,... 

The true stress at fracture calculated using the area based on the fracture surface results in a value that IS 80°i of that found using the diameter prior to fracture... 

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