PSI - Issue 14

A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 684–687 Author name / Structural Integrity Procedia 00 (2018) 000–000

685

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1. Introduction Near threshold fatigue crack response is extremely sensitive to load sequence effects. It is associated with the influence of near-tip stress on instantaneous resistance of crack tip surface layers to failure under atmospheric conditions (Brittle Metal Fracture model Sunder (2005)). As a result threshold stress intensity can be considered as not a material constant, but a variable which changes its value cycle by cycle depends on near-tip stress state response Sunder (2007), Sunder (2012). Therefore, an effective algorithm for stress calculation at the crack tip becomes significant problem in fatigue application. Traditional approaches which are well-known in notch fatigue analysis can be implemented in context of local inelastic response of crack tip. These methods involve solving Neuber equation or another rule for local inelasticity in combination with Ramberg–Osgood equation after accounting for material memory through Massing hypothesis. Using direct expressions for stress-strain relationship brings some limitations in material cyclic response, creep effects or cyclic unstable materials cannot be considered. Another disadvantage of such approaches is that they can be effectively used only for simple load sequences. The paper mainly deals with computational aspects of stress and strain distributions at the crack tip. A new approach is proposed to obtain near-tip stress under variable amplitude loading. 2. Proposed algorithm 2.1. Calculation strategy As LSS approaches attend to get direct analytical expression for local stress increment during cyclic loading and then apply material memory rules, we propose alternative computational procedure:  Calculation of stress intensity range 1   n K on current half cycle;  Determining of local strain increment at the crack tip * 1 ε   n ;  Calculation of local stress * 1 σ   n according to the accepted plasticity model. This algorithm is similar to the same used in finite element analysis (FEA) except strain calculation which is obtained from some approximation rule instead of variational formulation in finite element approach. In this paper we accept only linear rule in determining strain increment:

K n



(1)

ε   *  1 n

,

1



2 * 

r E

* r — physically possible minimum distance from the crack tip for stress calculation Sunder, E — Young modulus. Other strain approximation techniques also can be implemented (ESED method, etc.). Main advantage of proposed scheme is that all applicable in FEA material models can be considered. Fig. 1 shows graphical presentation of proposed algorithm in case of Al2024-T3 alloy for constant amplitude loading after tensile/comprehensive overloads. 2.2. Material model implementation

* 1 σ   n is closely connected with material response during cyclic loading. A lot of

Calculation of stress increment

mechanical effects (Bauschinger effect, ratcheting, cyclic hardening/softening, etc.) should be taken into account to provide adequate simulation results. Therefore appropriate hardening plasticity model need to be accepted. Further, we consider additive decomposition of total strain into elastic and plastic parts: