PSI - Issue 42

Mark Kachanov et al. / Procedia Structural Integrity 42 (2022) 96–101 M.Kachanov, V.Mishakin, Y.Pronina / Structural Integrity Procedia 00 (2019) 000–000

98

3

,       

1 1 2 2 K K K G G G         1 1 2 2 , V V

1

1

 

 

1

2

1

2

,

 

 

K K K G G G

1

2

1

2

R

R

where 1  and 2  are volume fractions of the phases ( 1 2 1     ) and subscripts V and R refer to the Voigt and Reuss bounds, respectively. We note that the width of the bounds is proportional to square of the contrast between the constituents’ properties:   2 1 2 G G Taking the mid-point provides accuracy that depends on volume fractions of the phases; even in the worst case of equal volume fractions, the mid-point provides accuracy of the order of several percent if the elastic contrast between the phases does not exceed 70—100% — as is the case for the considered austenite-martensite mixture. In our case of relatively low volume fraction of the martensite phase, the accuracy is even higher. Importantly, the mentioned estimates are insensitive to constituents’ shapes. As noted by Kachanov (in print), these facts lead to significant simplifications in the context of the considered material. Namely, they justify (I) neglection of shapes of the martensite particles, thus making the information on their volume fraction (provided by the eddy current data) sufficient, and (II) neglection of interactions between the particles. 3. Experimental data The low-cycle fatigue experiments were done on several samples made of the metastable austenitic steel AISI 321, for strain ranges varying from 0.5% to 1.4%; for details see works of Mishakin et al. (2021) and Kachanov et al. (2021). In the framework of micromechanics modeling, we focus on monitoring the evolution of crack density  and the dependence of its critical value *  at the fracture point on strain range and on the relative volume  of the martensitic phase. Remark. The usual definition of the crack density parameter   3 1 k V a    ( k a are the crack radii and V is the averaging volume) assumes that cracks have the circular (penny) shapes, whereas their actual shapes are “irregular” and diverse. Therefore,  should be understood as certain measure of crack density that may not have direct geometrical interpretation so that, when relating  to  , the latter has the meaning of “equivalent” crack density, i.e. the density of a set of circular cracks producing the same effect on the overall properties. Although the loss of the direct link to microgeometry may be undesirable, such interpretations, in explicit or implicit forms, are common in material science applications. An essential part of the experimental determination of  was finding the part   of the change of the effective Poisson ratio that is due to microcracking. This was done by subtraction from the overall change  (obtained by the acoustic technique) the contribution m  of the martensitic phase (its volume fraction being monitored by the eddy current technique) and the contribution of the change inc  at the incubation stage of fatigue (as discussed by Mishakin et al. (2021) and Kachanov et al. (2021)). The relation between   and microcrack density  was established in two ways: 1 1 2 2 G G     . V R G G  