An Investigation On Crack Tip Opening Stress Considering Thickness Effect

With the development of ship design and construction level,fatigue and fracture become the common failure forms of ship and ocean engineering structures.Under cyclic loading,a plastic zone is formed at the crack tip and a plastic zone wake is formed on the crack surface with the crack propagation.The crack closure phenomenon would occur while crack propagated because of the existence of plastic wake.The crack closure theory believes that only the portions of crack fully opening contribute to the crack propagation in cyclic loading.Therefore,the crack opening stress is significant to the evaluation of the growth rate.In order to accurately evaluate the fatigue life of cracked components,quantitatively calculating the crack opening stress is a vital question to be solved.Presently,the analytical method is based on some theoretical assumptions,most of which is derived under plane conditions.Besides,the experimental models can only be applied to the material and load conditions under the corresponding conditions.And most numerical methods need to analysis the crack tip filed,which costs too much in engineering.As a result,the existing models calculating opening stress can’t be wildly applied in engineering,and especially can’t put thickness effect into consideration.In this paper,the fracture parameter maximum crack opening displacement of midplane which is far away from the crack tip,considering the influence of the plate thickness,is introduced to study opening stress and crack growth rate based on the crack closure theory by fracture mechanics analysis,three-dimensional elastoplastic finite element analysis and experimental verification.First,the relationship between the maximum opening displacement amplitude and the opening stress of midplane is inferred by the theoretical analysis,and the computational model between two parameters is established based on the result of three-dimensional elastoplastic finite element analysis under constant amplitude cyclic tensile load.Then the model is modified through a series of finite element analysis in order to be applicable to different thickness,tensile load peak,initial crack length,yield strength,Young’s modulus,stress ratio and strain-hardening material.Based on the crack closure theory,the opening stress is calculated with the maximum crack opening displacement amplitude as the main parameter,and the effective stress intensity factor amplitude is obtained.The crack growth rate is predicted and compared with the experimental data,which proves the validation of the opening stress calculation.The effective stress intensity factor amplitude is used to describe the fatigue crack growth rate of specimens with different thickness,and the data can be condensed into a single curve,which provides a reference for evaluating the crack growth rate in engineering.Finally,under constant amplitude cyclic tensile and compressive load,the influence of compressive load on the opening stress of the midplane is quantitively studied.Combined with the model proposed under cyclic tensile load,a computational model of the opening stress with the maximum opening displacement as the main parameter is established.Through a series of finite element analysis,the influence of the tensile and compressive load peak,the initial crack length,yield stress,Young’s modulus and the strain-hardening material were studied.The influence of the Bauschinger effect on the crack closure was observed as well.The effective stress intensity factor amplitude during crack propagation is obtained by the model and the fatigue test data,which can condense the data of different non-normal stress ratios or different specimen thickness into a single curve.In this paper,a model to calculate the opening stress from the maximum crack opening displacement amplitude is proposed,which can provide a reference for calculation of opening stress considering thickness and the rapid prediction of fatigue crack growth rate in engineering.