TMM4175 Polymer Composites

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Questions and problems¶

Basic concepts¶

1) As simple and precise as possible: What is the meaning of the load proportionality factor?

2) As simple and precise as possible: What is the meaning of the exposure factor?

3) As simple and precise as possible: What is the basic idea of the maximum stress criterion?

4) Why should shear stresses be considered as absolute values in (any) stress based failure criteria?

5) Estimate the stress exposure factors based on both Maximum stress and Tsai-Wu criteria for the 3 different stress states a, b and c indicated in the figure below (that is; the red dots):

Computational problems and procedures¶

6) Derive the parameters $F_{1}, F_{11}$ and $F_{44}$ in the Tsai-Wu criterion

7) Find (estimate) the basic strength parameters $X_T,X_C,Y_T$ and $Y_C$ from the Tsai-Wu failure envelopes below. Then, compute the shear strength $S_{12}$. The Tsai-Wu interaction coefficients are $f_{12}=f_{13}=f_{23}=-0.5$

8) Find (estimate) the basic strength parameters $Y_T, Z_T, Y_C$ and $Z_C$ from the Tsai-Wu failure envelopes below. Then, explain how the basic strength parameters $X_T$ and $X_C$ can be derived from the envelopes. The Tsai-Wu interaction coefficients are $f_{12}=f_{13}=f_{23}=-0.5$

9) Consider the IFF part of the Hashin criterion, equation (3). Assume that the only non-zero stresses are $\sigma_2, \sigma_3$ and $\tau_{23}$ a) Simplify the equation (3) b) Consider the a stress state $\tau_{23} \ne 0$ while $\sigma_2 = \sigma_3 = 0$ , and find the expression for the exposure factor c) Rotate the stress in b) about the 1-axis by a random angle, and show that the exposure factor is identical to the one you found in b), and independent of the transverse tensile strength ($Y_T$).

10) Reduce the Hashin criterion to a plane stress case where the 3-axis is normal to the plane and implement the result in a python function for later use.

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