Maximum principal strain

In order to apply the crack nucleation approach, the mechanical state of the material must be quantified at each point by a suitable parameter. Traditional parameters have included, for example, the maximum principal stress or strain, or the strain energy density. Maximum principal strain and stress reflect that cracks in rubber often initiate on a plane normal to the loading direction. Strain energy density has sometimes been applied as a parameter for crack nucleation due to its connection to fracture mechanics for the case of edge-cracked strips under simple tension loading. ... 

Based on comparison of three traditional equivalence parameters with cracking energy density, the maximum principal strain corresponded the closest to the cracking energy density. Thus, Mars and Fatemi judged that the maximum principal strain is the most robust and meaningful of the traditional parameters considered in their work. 

Figure 17. Strain concentrations due to irregularities at the electrode and membrane interfaces. Circled sites on the right figure are locations with maximum principal strain greater than 15%.

The maximum principal strain criterion for failure simply states that failure (by yielding or by fracture) would occur when the maximum principal strain reaches a critical value (ie., the material s yield strain or fracture strain, e/). Again taking the maximum principal strain (corresponding to the maximum principal stress) to be 1, the failure criterion is then given by Eqn. (2.4). 

It is currently not well established which failure model is most appropriate for predicting failure of fluoropolymers that are monotonically loaded to failure. Commonly used approaches include the maximum principal stress, the maximum principal strain, the Mises stress, the Tresca stress, the Coulomb stress, the volumetric strain, the hydrostatic stress, and the chain stretch. In the chain stretch model, the failure is taken to occur when the molecular chain stretch, calculated fromPl... 

Analogous to principal stresses, there are principal strains acting on the principal planes of the strains. Also as in the principal stresses, the shear strains on the principal planes of those strains equal zero, i.e., the normal strains on these planes are actually the principal strains. Following convention, the maximum principal strain of the three is called the major principal strain , while the smallest strain is known as the minor principal strain . In an isotropic elastic material, the principal planes of strain coincide with the principal planes of stress. In a manner similar to that in Eqs. (1.22e) and (1.23), it is possible to write the following for the strain ... 

Fig. 16. The Maximum Principal Stress (a) and Maximum Principal Strain (b) state in the first analysis model for denture with Eclipse material...

No experimental data were available for the aluminium or the mixed joint at 180°C, and only two joints were analysed at this temperature for the FM350NA adhesive. It was thought that the errors in this case could be attributed to the fact that a maximum stress rather than maximum strain criterion had been applied. Given that the FM350NA undergoes reasonable plastic strain at the elevated temperature it may have been more appropriate to use a maximum principal strain criterion. 

Nonlinear Seismic Ground Response Analysis of Local Site Effects with Three-Dimensional High-Fidelity Model, Fig. 4 Distribution of time-history maximum values of norm of displacement and maximum principal strain... 

Fig. 41. Double-lap joint load versus maximum principal strain in adhesive 12 7 mm overlap 0-13 mm adhesive thickness (from Adams, Coppendale and...

If we now allow for non-linear adhesive behaviour, the high adhesive stress concentrations predicted by the linear elastic analysis will be relieved to some extent. Figure 54 shows the predicted spread of the yield zone of adhesive at the tension end of a double-lap joint as the load is increased. As would be expected, plastic flow begins near the adherend corner and the load corresponds to a joint efficiency of 21%. Each subsequent load increment represents an increase in joint efficiency of 4 4%. When elastic perfectly-plastic behaviour is assumed for the adhesive, a maximum strain criterion for failure seems appropriate. In Fig. 55 the joint efficiency is plotted against the maximum principal strain in the adhesive at each end of a double-lap joint. Assuming a failure strain for the adhesive of 5%, the analysis predicts a joint efficiency of 31% for a double-lap joint compared with 16% predicted by the linear elastic analysis. Similarly, the non-linear analysis predicts an efficiency of 39% for the double-scarf joint compared with 20% predicted by the linear elastic analysis. Although the predicted efficiencies are almost doubled by allowing for non-linear behaviour in the adhesive, failure in the adhesive is still predicted to be more probable than failure in the adherends (Table 5). 

Fig. 55. Joint efficiency plotted against adhesive maximum principal strain in CFRP-CFRP double-lap joint (from Adams, 1981).

A similar approach was proposed by Khoramishad et al. (2010a) in which the rate of damage was related to the maximum principal strain rather, than the equivalent strain and a threshold strain, Sth, was used rather than a plastic strain in order to define a strain helow which fatigue damage does not occur. 

Figure 12.8 Different repair conditions of the grouted sleeve and the corresponding predicted highest maximum principal strain in the pipe.

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