PSI - Issue 18

Matus Margetin et al. / Procedia Structural Integrity 18 (2019) 663–670

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Matus Margetin at al./ Structural Integrity Procedia 00 (2019) 000–000

1. Introduction In general components working in real operation are loaded with variable amplitude loading. In case of general shaped parts, the loading conditions create multiaxial stress state in critical places. These loading signals can be measured (Chmelko at al. 2015) or simulated using FEM (Kepka at al. 2018) and used for fatigue lifetime estimation. While fatigue lifetime estimation of component loaded with multiaxial variable amplitude loading signal is extremely complex task, the one of key aspects of this process is correct usage of multiaxial damage criterion. Nowadays most widely used multiaxial criteria are based on critical plane definition. The estimated fatigue lifetime is determined by damage accumulated in specific plane which is called critical plane. Exact definition of plane orientation varies from criterion to criterion and has crucial influence on accuracy of estimated fatigue lifetime. The aim of this paper is to investigate influence of critical plane orientation on fatigue life estimation of component loaded with multiaxial variable amplitude loading signal.

Nomenclature τ cr,a

shear stress amplitude acting on critical plane shear strain amplitude acting on critical plane σ n,max maximal normal stress acting on critical plane σ n,a normal stress amplitude acting on critical plane σ c-1 normal fatigue limit τ c-1 shear fatigue limit σ u ultimate stress σ y yield stress τ f ` shear fatigue strength coefficient b τ shear fatigue strength exponent D accumulated damage γ cr,a

2. Critical plane orientation Wide range of criterions based on critical plane theory have been introduced in recent years. These use multiple approaches to critical plane orientation definition. Based on that we can divided them into two groups. First group consists criteria, that based critical plane orientation on maximal damage acting on plane. The second group is formed by criterions with predetermined critical plane orientation. 2.1. Plane orientation defined by maximal damage The critical plane orientation in this case is defined by maximal damage parameter calculated on the plane. To find the critical plane orientation the calculation is needed in all possible plane orientation. The main benefits, from nonproportional variable amplitude loading perspective, is that the definition of critical plane orientation in case of variable amplitude loading is consistent with the fundamental definition of critical plane orientation in the case of proportional loading. In case of nonproportional variable loading the damage is accumulate in each plane and the plan with maximal accumulated damage will be considered as critical plane. The well-known criterion from this category is Findley criterion. Findley (1957) define its criterion as a linear combination of shear stress and normal stress acting on the plane: ���� � �� ����� � � (1) τ cr,a is the shear stress amplitude acting on the plane, σ n,max is maximal normal stress acting on the plane during loading cycle, f is the fatigue limit (in the case of finite life time calculation f represents the fatigue curve) and k is