Mixed mode crack KI, KII on pipe wall subjected to water hammer modeled by four equations fluid structure interaction


N. Brahmia,D. Daas,




Water hammer,transient flow,method of characteristics,finite differences,strain energy density,


In this paper, we studied the failure of the pipe during the transient flow. The pipe is made of ductile cast iron. To simulate the flow, a model includes an upstream tank connected to pipe with a valve at the end is presented; the transient flow is caused by fast time closure of the valve. The governing equations of water hammer are given from the mass and movement continuity conservation laws for fluid and mechanical behaviors laws for pipe structure. This mathematical model is a system of nonlinear hyperbolic partial differential equations where have solved by the method of characteristic along finite difference schema. To understand the behavior of material against surge pressure, we introduce the strain energy density theory (SEDT) S. The available mechanical propriety of ductile cast iron is used from previous study to get the critical value of strain energy density Sc. At the variance of stress intensity factor KIC criterion, the benefit of strain energy density S; that it can predict the crack growth initiation and direction when the applied stress does not coincide with the crack plane.


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