 ## General

#### With Paris law why does the crack propagate even for a very small amount of force?

• FAQ
Participant

For SMART and XFEM crack growth methods, we don’t have a ‘threshold’ value to specify for min(delta(K)) for cracks to start to propagate. If you look at Figure 3.1 https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v190/ans_frac/franundcgrowmech.html you will see three regions identified (Region I, II, and III). Paris’ law is da/dN = C delta(K)^m which only describes Region II. We don’t directly simulate Region I and III. The customer’s question below is probably asking about Region I, where in Figure 3.1, you see “delta(K)_th”, the minimum value at which a crack is assume to start propagating. Region I is not described by Paris’ law – in the chart, we plot da/dN vs. log(delta(K)), so you can see the equation we use would not work since Region I is not a straight line. Usually, customers interested in fatigue crack growth are interested in number of cycles to failure. Instead of thinking about min(delta(K)) for cracks not to propagate, we can think of a max(delta(N)) for cracks not to propagate for a given delta(a). For example, if the service life of a part is 10 million cycles and, for a given crack increment (delta(a)) ANSYS Mechanical is computing 1000 million cycles, we can assume that the crack won’t grow to delta(a). The main point is that Paris’ law is used, so no threshold for delta(K) is used. However, if the user can assume that the use of Paris’ law is appropriate for their application, they would look at delta(N) to determine if the crack will grow a given amount (delta(a)) for the number of cycles they are interested in examining. 