On the determination of material parameters in crack initiation laws

Abstract

A B S T R A C T Crack initiation along slip bands can be described by the Tanaka-Mura relation and its extensions. These relations are based on dislocation theory and determine the number of load cycles to reach a critical dislocation density for a given value of the resolved shear stress along the potential crack path. An important material parameter in these relations is the critical shear stress which is a threshold value for crack initiation, i.e. the number of cycles to crack initiation becomes infinitely high if the resolved shear stress along the potential crack path stays below this threshold value. This critical shear stress is determined using a database for microcrack initiation, microcrack growth, and coalescence obtained with a martensitic steel. The number of cracks per unit area, the so-called crack density, was derived from this database as a function of the number of load cycles. These experimentally observed values of the crack density are compared to values obtained by simulating the crack initiation process using a random cell structure as a mesoscopic unit cell. A best fit is obtained for values of the critical shear stress between 110 and 160 MPa with the uncertainty both related to simplifications in the model and to limitations of the experimental analysis.

Characterizing the Fatigue Damage in a Martensitic Spring Steel

“…The same issues were also reported in other studies. [8,10,15,34] Figure 7 shows the crack density as a function of the number of cycles for three different stress amplitudes. The crack density rises in all three cases with increasing number of cycles, indicating an accelerating fatigue damage evolution with increasing N and Δσ/2.…”

“…The same interrelation was determined in previous studies. [4,8,9,13,24] Furthermore, the fatigue long crack propagation, identifiable by an appreciable increase in the crack length, starts earlier at higher stress amplitude applied. Consequently, an incubation phase for fatigue crack growth could be observed, which seems to have the most significant fatigue life fraction at low stress amplitude.…”

On Tanaka‐Mura's fatigue crack nucleation model and validation

“…If the true strain were used in Equation , one would find an additional physical dimension of [m] 4 on the right‐hand side of the equation, which would not be correct. Actually, the stress‐based version (Equation ) is most often used in engineering analyses for real materials . But, in those analyses, the surface energy w s is often termed as the “specific fracture energy” that is often given arbitrary values (other than independently assessed) to fit the fatigue curve, eg, in Tryon and Cruse, w s = 440 kJ/m 2 for stainless steel, and in other works, w s = 2 kJ/m 2 for a martensitic steel.…”

“…Actually, the stress-based version (Equation 3) is most often used in engineering analyses for real materials. [6][7][8][9] But, in those analyses, the surface energy w s is often termed as the "specific fracture energy" that is often given arbitrary values (other than independently assessed) to fit the fatigue curve, eg, in Tryon and Cruse, 6 w s = 440 kJ/m 2 for stainless steel, and in other works, 7-9 w s = 2 kJ/m 2 for a martensitic steel. These values are orders-of-magnitude higher than the surface energies of metals, reported by Tyson and Miller.…”

Statistical analysis of damage evolution with a new image tool

“…In particular, special chosen cracks were analysed in more detail as the zigzag micro crack in Besel et al 1 . Other studies of damage evolution used simple quantitative approaches as analysing crack numbers, crack densities or crack orientations 2,3 . However, these studies were restricted to few cracks because the cracks had to be marked by hand.…”