Maximum strain criterion

If the fibres are aligned at 15° to the jc-direction, calculate what tensile value of Ox will cause failure according to (i) the Maximum Stress Criterion (ii) the Maximum Strain Criterion and (iii) the Tsai-Hill Criterion. The thickness of the composite is 1 mm. 

A single ply glass/epoxy composite has the properties Usted below. If the fibres are aligned at 30° to the x-direction, determine the value of in-plane stresses, a, which would cause failure according to (a) the Maximum Stress criterion (b) the Maximum Strain criterion and (c) the Tsai-Hill criterion. 

As the second term is less than 1, a tensile failure in the 2-direction would be expected, (b) Maximum Strain Criterion From the data given... 

A possible adjunct to the laminate design procedure is a specific laminate failure criterion that is based on the maximum strain criterion. In such a criterion, all lamina failure modes are ignored except for fiber failure. That is, matrix cracking is regarded as unimportant. The criterion is exercised by finding the strains in the fiber directions of each layer. When these strains exceed the fiber failure strain in a particular type of layer, then that layer is deemed to have failed. Obviously, more laminae of that fiber orientation are needed to successfully resist the applied load. That is, this criterion allows us to preserve the identity of the failing lamina or laminae so that more laminae of that type (fiber orientation) can be added to the laminate to achieve a positive margin of safety. 

The denominators in the first two of Eqn (6.34) are the tensile or compressive ultimate strains in the corresponding direction depending on whethCT or ey are tensile or compressive, respectively. It should be noted that for a material that is linear to failure, the predictions from the maximum strain criterion would differ from those from the maximum stress criterion only by a factor depending on the Poisson s ratios and Vyx- As with the maximum stress criterion, the maximum strain criterion provides some feedback on the type of failure mode occurring. 

A conservative design approach is to identify a maximum strain criterion of 0.2%. 

Generally, as the adhesive seems to be mainly a strain limited material the best failure criterion for a combined loading would be some strain based failure criterion such as the maximum strain criterion. 

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. 

The maximum strain criterion is becoming popular for plastics materials subjected to long-term loads upper strain limits for representative plastics are suggested in Table 2.2. Thus the appropriate design stress at a particular time and temperature can be found in the relevant creep data. 

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). 

Mechanical Behaviour of Composites (ii) Maximum Strain Criterion... 

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