Local Stress Intensity Research Articles

Study of the mechanical behavior and multiscale simulation of the crack propagation in a bilinga wooden beam

The mechanical behavior of local wood species (Bilinga) in the south west region in Cameroon during rainy and dry seasons and the mechanical behavior of wooden beam under bend loading are studied. The three points flexural tests were used to determine the mechanical properties of the wood under study. ANSYS 2020 R1 finite element (FE) software is used for numerical simulations at a macroscopic level using one of the newer technologies called Smart crack growth, which was introduced in the 2019 version. The geometry was modeled in SolidWorks with an initial crack length of 4 and 8 mm introduced in each sample and then imported to ANSYS workbench for further analysis with ANSYS which has all the tools to perform linear fracture. The stress intensity factor (SIF) determines the fracture toughness of a material which is subjected to linear-elastic fracture mechanics (LEFM) where a variable of the critical stress intensify is denoted as KIc. The fatigue crack growth was modeled using Paris’ law. The crack growth was simulated based on Mode I crack specimen with an initial crack length of 4 and 8 mm, respectively. The stochastic multiscale modeling of crack growth on meso- and microscale is used to compare the crack growth rate in the approach of a heterogeneous material and taking into account the microstructure and fracture mechanism of the Bilinga wood. The results of stochastic modeling of the crack growth in the array of cracks and pores of a characteristic size shows that the simulation is close to FE-modeling results. Therefore, the stochastic simulation of the crack growth in wood at meso- and microscale shows the lower local stress intensity factors and slower crack growth due to the existence of the scale-time hierarchy. The crack growth rate vcr at a macroscale ranges within 0.845 – 0.9 × 10–3 m/sec which corresponds to the macroscopic value of the fracture toughness KIc.

Singular integral based closed-form solutions for modified EMPS models in semipermeable magneto-electro-elastic materials

The singular integral equation method is applied to present analytical solutions for modified electric-magnetic-polarization saturation (EMPS) models subjected to semipermeable center cracked magneto-electro-elastic (MEE) materials. A generalized methodology is presented to explicitly solve the EMPS model under any arbitrary saturated electric and magnetic conditions using the distributed dislocation method (DDM) and finding the analytical solutions for developed singular integral equations. The explicit expressions are derived for distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), saturated zone lengths, and local stress intensity factor (LSIF) for particular cases of the generalized EMPS model such as constant, linear, quadratic and cubic polynomial varying saturated electric and magnetic conditions. Using an iterative scheme and the explicit solutions of COD, COP, and COI, the exact semipermeable crack-face conditions are evaluated at the center of the crack, and the same applies throughout the crack-surface for the study of semipermeable modified EMPS models. A comparative analysis of the fracture parameters has also been carried out between the results of exact semipermeable crack-face conditions and the results of semipermeable crack-face conditions of the center crack problem to analyze the impact of polynomial varying saturated conditions on the crack-face conditions. Numerical studies performed under different electromagnetic-mechanical loadings, volume fractions, and crack-face conditions demonstrate the increasing effects in the fracture parameters' values with the degree of the polynomial varying saturated conditions.

3D characterization of closure of surface and internal fatigue cracks in nodular cast iron using Digital Volume Correlation of laboratory X-ray tomography images

Digital volume correlation (DVC) of laboratory X-ray tomography images has been used to characterize the closure of artificial internal fatigue cracks in nodular graphite cast iron. DVC allows to produce crack opening displacement (COD) map from 3D tomography images at the sub-voxel scale thanks to the graphite nodules which can be used as internal natural markers. Fatigue samples containing controlled internal defects have been produced in a nodular cast iron by diffusion bonding plates containing laser-machined sharp notches. Specimens with internal cracks and surface cracks were respectively characterized by laboratory tomography at different loads during fatigue crack propagation tests. The local stress intensity factors (SIFs) have been extracted from the measured displacement fields by using Williams series, based on those results the closure levels of internal cracks and surface cracks were comparatively analyzed and discussed. Crack closure levels were found to be linearly related to the location of the surface crack front, and the level of internal crack closure was comparable to that of the surface crack in bulk.

High-cycle and low-cycle fatigue life prediction under random multiaxial loadings without cycle counting

A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers.

A multiscale fracture model to reveal the toughening mechanism in bioinspired Bouligand structures

The Bouligand structure has been observed in a variety of biological materials, such as lamellar bone and exoskeleton of lobsters. It is a hierarchical and non-homogeneous architecture that exhibits excellent damage-resistant performance. This paper presents a multiscale fracture model considering the material inhomogeneity, the multiscale property, and the anisotropy to reveal the toughening mechanisms in the Bouligand structure. Firstly, the macro and micro constitutive properties of this composite are derived. Then, a multiscale fracture model is developed to characterize the local stress intensity factors and the energy release rates at the crack front of twisted cracks. Our results demonstrate that the decrease in the local energy release rate can be attributed to two-step mechanisms. The first mechanism is that the multiscale structure and the material inhomogeneity cause a release of stress near the initial crack tip. The second mechanism is that the twisted crack leads to the transformation from single-mode loading to mixed-mode loading, which enhances the fracture toughness. These results can not only reveal the toughening mechanism of the Bouligand structure but also provide guidelines for the design of high-performance composites. Statement of significanceBiological materials in nature often possess excellent mechanical properties that have not been achieved by synthetic materials. Bioinspired Bouligand structures provide prototypes for designing high-performance materials. In this study, we propose a multiscale theoretical fracture model to investigate the fracture properties of Bouligand structures with twisted cracks. We systematically consider the roles of material inhomogeneity, anisotropy, and multiscale properties. Our analysis demonstrates that the remarkable toughness of Bouligand structures results from the combined effects of material inhomogeneity and twisted cracks. This research contributes to unveiling the secret behind the outstanding toughness of Bouligand structures and provides inspiration for the development of novel designs for man-made composites.

Singular integral method based closed form solution for moving EMPS model in semipermeable two‐equal‐collinear cracked MEE material

AbstractThis paper presents the analytical closed‐form solutions of moving two equal collinear semipermeable cracks in magneto‐electro‐elastic material considering the strip electric‐magnetic polarization saturation (EMPS) model. To simulate the dynamic/moving cracks problem, two equal collinear Yoffe type cracks moving with a constant subsonic velocity along the plane of the cracks is considered. The problem is solved by considering semipermeable crack face conditions and under the in‐plane electro‐magnetic‐mechanical loading. Applying distributed dislocation technique and symmetry of the collinear cracks, the problem is reduced into simultaneous singular integral equations which have been solved in closed form expressions using finite Hilbert approach. The explicit expressions for dynamic distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), and local stress intensity factors (LSIFs) are evaluated for both the cases of the EMPS model (magnetic zone is smaller or greater than electric zone). For evaluation of inner and outer electric and magnetic zone lengths (MZLs), an iterative approach is applied to solve the developed two non‐linear equations. Also, to implement the semipermeable crack‐face conditions, a bisection iterative method has been applied. Based on the developed closed form solutions, numerical studies are presented for standard fracture parameters with respect to crack propagation velocity, electrical loading and inter‐crack space distance. This study shows that electric displacement and magnetic induction defined over the crack‐surface for semipermeable conditions decrease whereas the numerical values of saturated zone lengths, COD, COP, COI, and LSIFs increase with increasing crack propagation velocity. Moreover, for both static and dynamic cracks problems, the significant crack‐interaction effects have been observed on all the studied fracture parameters except the crack‐face conditions.

Experimental investigation of process parameter variations on the microstructure and failure behavior of IN718 structures in PBF-LB/M

Conventional manufacturing technologies, such as milling or casting, are limited in terms of the manufacturable complexity of the parts to be produced. They are also restricted in terms of the local modifiability of the mechanical properties. Additive manufacturing, specifically the Powder Bed Fusion of Metals using a Laser Beam (PBF-LB/M), is a novel method, which is capable of addressing both limitations. However, the resulting parts are often prone to cracking during PBF-LB/M and in the service afterward because of high thermally induced local stress intensities. Selectively modifying the process parameters during the fabrication can be a suitable strategy to locally reduce the failure susceptibility. Over the course of this study, samples made from the nickel-based superalloy Inconel 718 were manufactured with varying laser powers, hatch distances, and scan speeds. The samples were divided into stress crack specimens as well as static and dynamic tensile test specimens. The grain structure was investigated, and correlations between the microstructure and the cracking susceptibility were determined. It was found out that variations in the laser power had the most pronounced effect on the grain structure and the failure behavior. An increasing grain size enhanced the fracture resistance in the stress crack samples while the static and dynamic mechanical properties deteriorated. Based on these results, the application area of PBF-LB/M could potentially be widened due to the manufacturability of parts otherwise susceptible to stress-induced cracking. The mechanical properties of as-built parts can remain unchanged utilizing a local process parameter adaption.

Sub-size specimen testing for near-threshold fatigue crack behaviour of additively manufactured Ti-6Al-4V

Sub-size specimen testing offers a potentially elegant solution to accompany fatigue life assessments in determining vital fatigue parameters such as effective fatigue crack growth propagation thresholds (ΔKth,eff). Additively manufactured parts stand to benefit from this in potential build-by-build fatigue validation without foregoing process-inherent material saving and low lead times. In this study, sub-size Laser Powder Bed Fusion (LPBF) produced Ti-6Al-4 V SENB specimens built in two orientations with stress relieved and annealed material states are considered. Scanning electron microscopy with electron backscatter diffraction is used to consider both meso- and microstructural features, complimented by digital image correlation (DIC) for determining local stress intensity and triaxiality around the crack tip. Results show inconsistent near-threshold fatigue behaviour linked to the microstructure of annealed material, where the fatigue threshold in sub-size specimens is reduced. Furthermore, reducing specimen size influences both in- and out-of-plane crack tip constraint, with higher constraint experienced by the sub-size specimens. Overall, this study presents and discusses the domain and suitability in using sub-size specimen FCGR threshold testing for LPBF produced Ti-6Al-4 V builds considering their unique meso- and microstructural features.

Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique

AbstractIn this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.

Fatigue analyses and life predictions of copper laser-welded lap-shear samples

This study experimentally and numerically investigated the fatigue response of laser-welded (LW) lap-shear samples in copper (Cu) sheets of dissimilar thicknesses. Fatigue tests were first conducted, and the resulting fatigue data and failure modes were recorded. To investigate the failure processes and mechanisms, microscopic examinations, including microhardness tests for Cu LWs, were conducted before and after the failure. The experimental results showed the interfacial failure under high-load-range and low-load-range conditions and the top sheet separation under median-load-range conditions. Next, finite element analyses for LW lap-shear samples were conducted to calculate the global stress intensity factors (GSIFs) and local stress intensity factors (LSIFs) for interfacial and kinked cracks, respectively. The GSIFs, LSIFs, and Paris law were further used to derive the two fatigue models to analyze the evolution of interfacial and kinked cracks, respectively. Finally, two fatigue models estimated a series of fatigue lives that matched the general trends of experimental data.

A microstructure-sensitive analytical solution for short fatigue crack growth rate in metallic materials

Short fatigue crack growth in engineering alloys is among the most prominent challenges in mechanics of materials. Owing to its microstructural sensitivity, advanced and computationally expensive numerical methods are required to solve for crack growth rate. A novel mechanistic analytical model is presented, which adopts a stored energy density fracture criterion. Full-field implementation of the model in polycrystalline materials is achieved using a crystallographic crack-path prediction method based on a local stress intensity factor term. The model is applied to a range of Zircaloy-4 microstructures and demonstrates strong agreement with experimental rates and crack paths. Growth rate fluctuations across individual grains and substantial texture sensitivity are captured using the model. More broadly, this work demonstrates the benefits of mechanistic analytical modelling over conventional fracture mechanics and recent numerical approaches for accurate material performance predictions and design. Additionally, it offers a significant computer processing time reduction compared with state-of-the-art numerical methods.

Probabilistic failure assessment of an irradiated DEMO breeding blanket component under ferromagnetic loads: Impacts of material data scattering and uncertainty in local stress intensities

The most significant technical challenge in developing structural materials for in-vessel components in the Demonstration Power Plant (DEMO) fusion reactor is to qualify the lifetime of material to guarantee the lifetime of components. The qualification needs to be conducted theoretically rather than empirically because it is conducted based on the knowledge and data acquired in fission neutron irradiation experiments and various simulation irradiation experiments rather than in experiments performed in the actual fusion environment. Such experiments will not be achievable until the DEMO fusion reactor becomes operational. Consequently, various uncertainties are expected in irradiation data and loading conditions.The probabilistic approach, where the probability of failure is calculated based on the probability density function of postulated load distribution and material property distribution, is one path to mitigate such uncertainties. In this approach, those probabilities constitute the subjective probability based on the theoretical understanding of fusion neutron irradiation effects on materials to maximize the confidence in the estimated value.A case study of the Japanese DEMO breeding blanket is the basis for the discussion of the technical issues involved in the probabilistic approach. The breeding blanket design was simplified, the failure probability was estimated, and the impact of electromagnetic force on ferromagnetic material caused by a strong magnetic field induced by toroidal field coils was considered. The discussion of the impact of the irradiation damage is based on the irradiation data for F82H reduced-activation ferritic/martensitic steel. A direction for the development of fusion structural materials is suggested in terms of design technology and the statistical quality of the irradiation database.

Defect-based characterization of the fatigue behavior of additively manufactured titanium aluminides

The additively manufactured titanium aluminide alloy TNM-B1 was characterized microstructurally and mechanically in the as-built and hot isostatically pressed (HIP) condition. Tensile and constant amplitude tests were performed at room temperature and 800 °C. Using fractographic SEM images, the fracture-inducing defect was identified. With the HIP, defect number and size could be reduced, increasing fatigue strength by 43% to 500 MPa. Using the model approaches of Murakami and Shiozawa, the fatigue life was correlated with the local stress intensity factor and could be described as function of the stress amplitude as well as the size and location of fracture-inducing defects.

The mechanical properties and fatigue responses of fiber metal nanocomposite laminates with double-edged cracks

ABSTRACT The fiber metal laminates (FMLs) of hybrid Ti/APC-2 neat and nanocomposite laminates were fabricated. Geometrically symmetric and anti-symmetric double-edged cracks were cut in FMLs. From tensile tests, we received the load vs. displacement curves, stress intensity factors of mixed mode and mechanical properties. From cyclic tests, the load vs. cycles (P–N) curves, residual life and failure mechanisms were obtained. The mechanical properties of symmetrically cracked specimens were slightly lower than those of anti-symmetrically cracked counterparts. As the crack length increases and inclination angle decreases, the fatigue life decreases. The enhancement of nanopowder improved the ultimate load and fatigue life. The local stress intensity at the crack tip dominates the fatigue responses. The piece of elliptical part was observed from cyclic tests at failure. Although the attraction of two crack tips accelerated the crack growth towards each other, the delay to failure was caused by two crack tips circling around and forming a small piece of ellipse centrally.

Dynamic effects and an oscillator model of a spatio-temporal representative volume describing fracture process at the crack

An analytical investigation of a fundamental dynamic fracture effect observed in samples with a crack under shock-wave pulse load is provided. Particular attention is paid to the phenomenon of delayed fracture. The effect can be described in the following way: the fracture in the crack tip vicinity can possibly take place after the local stresses reached their maximum value. A number of important features of dynamic fracture under the threshold and beyond threshold loads, observed in various experiments, are discussed. It was found that the experimentally registered fracture delay can be clearly explained within the framework of the structural-temporal approach based on the concept of the incubation time of fracture. The conditions for the delay are found and the corresponding analytical formulas are given. Additionally, a simple analogy based on a mass-spring model is discussed. Analytical formulas available for the oscillator model help to find some non-obvious similarities between the crack behaviour under short pulse loads and the oscillator failure due to analogous loads. It is concluded that it is essential to study threshold cases in which the most important time effects appear that do not fit into the classical concepts of strength and crack resistance – the concepts that rely on local ultimate stress and/or critical intensity factor parameters.

Crack propagation modelling for service life prediction of large slewing bearings

Slewing bearings in wind turbines are meant to last 20 years or longer. But wind turbine accidents (structural failure) occur nevertheless in some cases earlier. Minimizing the risk and with this enhancing the public acceptance of wind turbines is of great importance for the increase of alternative energy production. For a more accurate prediction of the service life of slewing bearings XFEM calculations with crack initiation and crack propagation are developed using Abaqus XFEM. The material parameters such as Paris coefficients for crack propagation and fracture toughness values (KIC) were measured in advance on samples of different heat treatment conditions. With a linear elastic fracture mechanics approach the local stress intensity factor range ΔK for a given starting crack front is calculated. Coupling this information with the Paris-law and a maximum crack propagation interval of 0.1-0.3 mm, the number of cycles to failure during crack propagation is determined. The crack is extended stepwise until ΔK reaches the limiting fracture toughness of the material. The crack propagation model was first validated on different test specimen geometries. Correlating these first simulated test results with experimental data the crack initiation phase can be estimated. The simulation of real components, such as bearings, will be developed subsequently, using calculated stress distributions provided by other partners in the project as input parameters (sub-structure approach). Fatigue tests are also done on pre-corroded specimens since bearing failure may also be promoted by an unfavorable combination of overloads and corrosion damage.

Qualification of uniform fatigue damage tolerance law for additively manufactured and cast Al-Si alloys

The demand on lightweight structures and materials are steadily growing in automotive and aerospace industries. Hypo-eutectic Al-Si alloys are promising candidates due to its high specific material strength and corrosion resistance. Near net shape manufacturing by additive manufacturing (AM) or castings allow a high resource efficiency. The complex geometries lead to a wide range of structural features due to process-induced variations in local cooling rate. Therefore, the relationships between structural characteristics (e.g. dendrites, grain, eutectic, porosity, lack of fusion) and fatigue behavior have to be understood to enable a lightweight and reliable design of Al-Si alloys. In this study, the effect of process and process-induced structural characteristics on stress-strain behavior (quasi-static, cyclic) and high cycle fatigue behavior were characterized. The specimens were processed by laser-based powder bed fusion (PBF-LB) and sand casting (SC) with variation in porosity and dendrite arm spacing. Hereby, the age-hardenable Al-Si alloys AlSi10Mg (AM, SC) and AlSi7Mg (SC) were investigated. AM batches were tested in as-built condition. All casting batches got a HIP densification and T6 heat treatment. The fatigue results were analyzed based on nominal stresses according to Woehler (S-N curve) and local stress intensity based on linear-elastic fracture mechanics (stress intensity factor) as well as elastic-plastic fracture mechanics (J integral). J integral based Shiozawa diagrams allowed a sufficient and uniform fatigue damage tolerance (FDT) assessment for all AM and SC alloys. Hereby, the FDT of Al-Si alloys were dominated by defects (size, position) and cyclic stress-strain behavior (yield strength, cyclic hardening).

Kinked and forked crack arrays in anisotropic elastic bimaterials

The fracture problem of multiple branched crack arrays in anisotropic bimaterials is formulated by use of the Stroh formalism to the linear elasticity theory of dislocations. The general full-field solutions are obtained from the standard technique of continuously distributed dislocations along finite-sized cracks of arbitrary shapes, which are embedded in dissimilar anisotropic half-spaces under far-field stress loading conditions. The bimaterial boundary-value problem leads to a set of coupled integral equations of Cauchy-type that is numerically solved by using the Gauss–Chebyshev quadrature scheme with appropriate boundary conditions for kinked and forked crack arrays. The path-independent Jk-integrals as crack propagation criterion are therefore evaluated for equally-spaced cracks, while the limiting configuration of individual cracks is theoretically described by means of explicit expressions of the local stress intensity factors K for validation and comparison purposes on several crack geometries. The short-range interactions resulting from the idealized configurations of infinitely periodic cracks are investigated as well as various size- and heterogeneity-effects on the mixed-mode cracks in complex stress-state environments. The influences of anisotropic elasticity, elastic mismatch, applied stress direction, inter-crack spacings and crack length ratios on the predictions from the Jk- and K-based fracture criteria are examined in the light of different configurations from the single kinked crack case in homogeneous media to the network of closely-spaced forked cracks in presence of bimaterial interfaces.

Analysis of prospective SIF and shielding effect for cylindrical rough surfaces obtained by L-PBF

Fatigue properties of parts built by Additive Manufacturing (AM) are strictly related to process-induced defects and complex surface morphology. Several studies have proved that surface valleys act as crack initiation sites, similarly to surface micro-notches. However, different roughness parameters have been considered in literature for the depth of the surface notches, together with the adoption of a shielding factor. The aim of this study is to understand how the surface complexity of L-PBF (Laser-Powder Bed Fusion) AlSi10Mg cylindrical specimens in as-built condition can affect the fatigue behaviour. In detail, CT (Computer Tomography) scans were adopted to characterize the surface quality and 2D FE (Finite Element) analyses were used to calculate the local stress intensity factor at the most critical valleys in the surface. The results of the FE analyses were compared with a shielding factor determined for regularly spaced notches. In spite of the significant scatter, the average geometric factor value for surface notches in L-PBF surfaces is correctly predicted by the traditional shielding factor.

Analyzing the influence of a deep cryogenic treatment on the mechanical properties of blanking tools by using the short-time method PhyBaLCHT

Deep cryogenic treatment (DCT) is a promising post-process for increasing the service lifetime of highly loaded tools. However, the process parameters as well as the position of DCT during thermal post-processing have to be adapted on the materials used, leading to high experimental effort, costs and time to optimize and validate this kind of thermal treatment. Therefore, efficient methods to analyze the mechanical properties of materials treated with DCT are of great industrial and scientific interest. In this context, the short-time method PhyBaLCHT, which is based on instrumented cyclic indentation tests, is a promising approach, as it enables a rapid determination of the cyclic deformation behavior and hardness of a material. Consequently, in the presented work different material conditions of the thermally treated tool steels 1.2379 (X155CrVMo12-1; AISI D2) and Vanadis 4E (140CrMoVMnSi19-35-37) were characterized by using cyclic indentation testing. The different conditions were realized by performing different sequences of thermal post-processing, containing quenching, tempering and DCT. The results obtained in cyclic indentation tests show for both materials slightly lower hardness but significantly higher cyclic plasticity of the material conditions treated with DCT antecedent to the tempering process compared to conventionally quenched and tempered material. In additionally performed blanking tests, this further results in an increased wear resistance of cryogenically treated conditions. Because of the higher cyclic plasticity, the reduction of local stress intensities at the cutting edges caused by plastic deformation is more pronounced for the cryogenically treated tools, which results in decreased wear rate as well as less pronounced breaking of the cutting edges. Consequently, the presented results demonstrate that the PhyBaLCHT method is a powerful means to characterize the mechanical properties of cryogenically treated materials and enables an estimation of the wear characteristics of highly loaded tools.