The Mechanism Research Of Crack Tip Opening Angle In Elastic Plastic Materials

In the damage tolerance analysis of thin-walled metal structures,such as aircraft wings and fuselages,stable crack growth plays quite an important role,and crack tip opening angle(CTOA)was shown to be the most suitable fracture parameter for simulating stable crack growth.Since the mechanism of CTOA is still unclear,CTOA was only considered as an engineering parameter so far.Therefore,the purpose of this dissertation is exploring the mechanism of CTOA in elastic plastic materials.The work of this dissertation can be divided into two parts: the application research of CTOA and the mechanism research of CTOA.The application part proposes a crack tip model in which the elastic plastic growing crack profile is considered as the corresponding stationary crack profile minus the height of the plastic wake.According to this model,a simple CTOA calculation method was proposed in which only the load-crack extension curve is required.Thus,critical CTOA can be measured by the static tensile tests of M(T)or C(T)specimen.Compared with the optical method provided by ASTM E2472,the proposed method is easier to measure and the test results are more convergent.The error between the proposed method and the ASTM E2472 method is less than 5%.In addition,the theoretical relation between critical CTOA and K-R curves was derived.According to this relation,the existing K-R curves can be transferred into the critical CTOA values corresponding to the same material and thickness,which will greatly enrich the database of critical CTOA.This relation has also shown that: For aluminum alloy,the critical CTOA will decrease with the increasing thickness,and the variation trend is not linear,the decreasing rate of CTOA is decreasing with the increasing thickness.Also according to the above crack tip model,critical CTOA criterion can be transferred into the “critical stationary opening profile” criterion.Critical stationary opening profile is the profile of a stationary crack which has the same crack length and applied load as a growing crack.On the basis of this,it is strictly proved by dimensional analysis that for given material and stress state,the critical CTOA is independent of in-plane geometry and load type.According to the“critical stationary opening profile” criterion,an analytical method was proposed to predict residual strength based on critical CTOA.In this method,the crack propagation behavior can be obtained only by the expression of stationary crack opening profile.The residual strengths of M(T)?C(T)and rivet stiffened panels were successfully predicted through this analytical method,the errors between calculated and test results are all less than 5%.The core thought of the mechanism research part is “the nature of crack growth is the formation of crack surface”.On basis of this viewpoint,a crack driving force parameter was defined,the product of this parameter and the crack tip velocity equals the power dissipated by forming new crack surfaces,the relation between CTOA and crack driving force was also derived.To avoid the Rice paradox,the crack tip was replaced with the fracture process zone,the power dissipated by forming new crack surfaces will then turn into the power dissipated by fracture process zone.On this basis,the relation between CTOA and crack driving force was derived.This relation not only proved that critical CTOA is a constant during stable propagation but also proved “crack tunneling” is one main reason of the initial non-constant CTOA phase.In addition,this relation proved that the value of critical CTOA depends on the micro-mechanism of fracture.When the thickness is large or small enough,the stress state will maintain plane strain or plane stress state,the micro mechanism of fracture will then be invariant,therefore,critical CTOA will be independent of thickness in this case.This part also proposed an opinion that crack growth is only governed by the local parameter.In this opinion,when crack propagates in elastic plastic materials,the work of external load will flow into the crack tip,in spite that most of these work are dissipated by plastic deformation,the crack expands whether or not depends entirely on whether the energy flowing into the crack is sufficient to form new crack surfaces,local parameter is the parameter that can characterize the forementioned process.It is strictly proved that the crack driving force parameter is a local parameter in this paper,and this parameter is equal to the projection of the crack tip configurational force into crack growth direction.In addition,the common elastic plastic fracture parameters were also found to be consistent with the above driving force parameter.According to the relationship between CTOA and crack driving force,CTOA is thus associated with these elastic plastic fracture parameters.Therefore,critical CTOA can characterize the growing crack tip fields.According to the energy dissipated by the fracture process zone,the theoretical relation between critical CTOA and cohesive zone model was derived.In order to verify the above relation,an equivalent cohesive zone model was proposed,the core idea of this model is that: For any cohesive zone model,an equivalent cohesive zone model exists,the dissipation energy and the traction separation law of the equivalent cohesive zone are identical to the cohesive zone one,but both the displacement and the displacement rate distributions on the equivalent cohesive region are linear,thus the length of the equivalent cohesive zone is different from the cohesive zone length.According to the equivalent cohesive zone model,the relation between critical CTOA and cohesive zone model was simplified.Three groups of data were used to verify the simplified formula.The maximum error between the values of critical CTOA derived from this theoretical formula and the test values is only 7.2%.