Issue 42

R. Pawliczek et alii, Frattura ed Integrità Strutturale, 42 (2017) 30-39; DOI: 10.3221/IGF-ESIS.42.04 33 This form of equation (Young modulus) suggests that mean stress is responsible for elastic part of deformation. However, the parameter ε apl in Eq.(4) is still undefined. Also to solve this problem, the Ramberg-Osgood equation can be used. Bearing in mind, that the shape of the stable hysteresis loop does not change for the same strain amplitude and different mean strains we can calculate stress amplitude σ a using relation 1 n a a a E K             (5) It is very important to use coefficients K’ = K’(ε m =0) and n’ = n’(ε m =0) obtained for standard, symmetric loading (ε m =0 and σ m =0) in the case of Eq.(4). All the equations presented above are adequate for cyclic load with the mean load, where load conditions are constant during the test. However, it was mentioned before, for block loading location of the hysteresis loop can be different for each segment of block. Some researches of this problem [11] allows observing, that changing the men load during test a new, stable location of the hysteresis loop is registered. Strong flow of the mean strains along strain axis usually arises at the end of life of the specimen, so it can be assumed, that each, new position of the hysteresis loop stabilises at new levels of mean strain and stress (Fig.3). Figure 3 : Location of the hysteresis loops for the next sequence in the block load. After first block, where strain ε m1 and stress σ m1 exists a new position of the hysteresis loop is observed and described by parameters ε m2(measured) and σ m2 . Notation “measured” means mean strain of the measured strain history. It should be noted, that after first sequence some value of permanent deformation ε Apl1 exists in material after unloading (Fig.3). This part of strains participates as the initial state of the material for next stage of loads. In the case, for which the second block will have zero mean load value it leads to situation, that presented algorithm will resulting with non-zero mean stress, what is not corresponds to the real stress conditions. The strain ε Apl1 as the “starting” point for each sequence must be taken into account in calculations. T HE ALGORITHM FOR STRESS HISTORY CALCULATION aving regard to the considerations presented above the following algorithm for stress history calculation can be defined, where all the steps must be repeated for each sequence in the block load for whole registered time history of the strain:  m1  m2  m1  m2(measured)  m2(real)  Apl1   H