Issue34

Z. Marciniak et alii, Frattura ed Integrità Strutturale, 34 (2015) 1-10; DOI: 10.3221/IGF-ESIS.34.01 6 K t Model Neuber  max (MPa) Molski-Glinka  max (MPa) Macha-Łagoda  max (MPa) 9.61 421 386 405 4.30 329 302 316 3.23 294 270 282 1.85 233 215 224 Table 1 : The presentation  max depending on K t and strain energy density models. Professor Macha was interested most in energy criteria of multiaxial random fatigue. In this field, in cooperation with Łagoda he proposed a generalised criterion of energy density parameter for normal and shear strains in critical plane, shown as [18, 20]   max ( ) ( ) ns n t W t W t Q     or max ( ) eq t W t Q      (14) where  ,  , Q – constants for the selection of a given criterion version. Guidelines of the proposed criterion are as follows [21]: “a) this portion of strain energy density is responsible for fatigue crack, which matches the work of normal stress  n (t) in normal strain  n (t), that is W n (t) and work of shear stress  ns (t) in a shear strain  ns (t) in the direction s in plane with normal n, that is W ns (t), b) direction s in the critical plane matches average direction, in which density of shear strain energy is maximal, c) in boundary state, material effort is determined by the maximum value of linear combination of energy parameters W n (t) and W ns (t).” For uniaxial stress state, strain energy density parameter is expressed as       sgn ( ) sgn ( ) ( ) 0.5 ( ) ( )sgn ( ), ( ) 0.5 ( ) ( ) 2 t t W t t t t t t t            . (15) For multiaxial stress state, the course of equivalent strain energy density parameter is calculated in the critical plane with normal n and shear direction s as     ( ) ( ) ( ) 0.5 ( ) ( )sgn ( ), ( ) 0.5 ( ) ( )sgn ( ), ( ) eq ns n n n n n ns ns ns ns W t W t W t t t t t t t t t               . (16) The proposed energy criterion in the critical plane is applicable for cyclic and random loads for small and large number of cycles. Depending on the coefficients chosen, different criteria are obtained and thus, for: -  = 0,  = 1 we have the criterion of maximum energy density for normal strain in the critical plane, -  = 1,  = 0 we have the criterion of maximum energy density for shear strain in the critical plane, -  = 1,  = 1 we have the criterion of maximum energy density for normal and shear strain in the critical plane. When applying energy fatigue criteria to assess life, energy characteristics are used, developed as a result of the Coffin- Manson-Basquin characteristic multiplication [22-24] by stress amplitude determined for specimen half-life. However, this characteristic not fully illustrates the behaviour of cyclically unstable materials. Being aware of these differences, Professor Macha and Słowik proposed a new model to determine energy fatigue characteristics directly from experimental research. This model is described as [25]       0.5 pl i W t t t       , (17) where  i pl =  (t i ) for  (t i ) = 0 and i = 1, 2, 3,.... are successive numbers of the hysteresis loop (σ-ε).