Shear strength factor

The shear strength factor f_τ$=\frac{Shear\; strength}{\mathrm{Tensile\; strength}}$ must be determined experimentally. It is dependent on the temperature, loading rate, moisture content, and multiaxiality of the material used in the component. The shear strength factor is used to determine the failure criteria. The Maximum Stress Theory is suitable for brittle materials. The Maximum Stress Theory assumes that material failure always occurs perpendicular to the direction of the greatest positive principal direct stress. The maximum distortion energy theory is applied for ductile materials. In this case, failure due to yield is decisive.

The shear strength factor ${\displaystyle f_{\mathrm{\tau <!--\; \tau \; -->}}}$ is considered in the interaction equation ${\displaystyle {\mathrm{\sigma <!--\; \sigma \; -->}}_v=q\cdot <!--\; \cdot \; -->{\mathrm{\sigma <!--\; \sigma \; -->}}_{V,NH}+(1-<!--\; -\; -->q)\cdot <!--\; \cdot \; -->{\mathrm{\sigma <!--\; \sigma \; -->}}_{V,Mises}}$ via the control parameter ${\displaystyle q=\frac{\sqrt{(}3)-<!--\; -\; -->(1/f_{\mathrm{\tau <!--\; \tau \; -->}})}{\sqrt{(}3)-<!--\; -\; -->1}}$. Thus, the resulting equivalent stress ${\displaystyle {\mathrm{\sigma <!--\; \sigma \; -->}}_v}$ is determined from equivalent stress according to the Maximum Stress Theory ${\displaystyle {\mathrm{\sigma <!--\; \sigma \; -->}}_{v,NH}}$ and the von Mises equivalent tensile stress ${\displaystyle {\mathrm{\sigma <!--\; \sigma \; -->}}_{v,Mises}}$.

Consequently, a value of ${\displaystyle f_{\mathrm{\tau <!--\; \tau \; -->}}=1.0}$ leads to pure equivalent stress according to the Maximum Stress Theory, and a value of ${\displaystyle f_{\mathrm{\tau <!--\; \tau \; -->}}=\frac{1}{\sqrt{(}3)}\approx <!--\; \approx \; -->0.577}$ to pure von Mises equivalent tensile stress.