Stress-strain Data Research Articles

Characterization of 3D Orthogonal Woven Carbon/Kevlar Composite Under Tensile Loading

In the present work, the tension response of polypropylene (PP) based composites reinforced with Carbon/Kevlar fabrics was investigated. The weft, wrap, and binder are considered in the direction (XYZ) and woven into a 3D fabric. Two homogeneous fabrics with Carbon (CCC), Kevlar (KKK), hybrid Carbon/Kevlar (CCK), and hybrid Kevlar/Carbon (KKC) fabrics were produced using a hand-made spoke frame. The architecture of the fabrics was three-dimensional orthogonal (3D-O). Four different composite laminates were manufactured using a vacuum bag-assisted moulding technique. The tensile loading was applied using a Nano-UTM set-up at travel of +6.25/-3.1 mm and software-automated generation of stress-strain data. The results indicated that the tensile properties of thermoplastic 3D-O composites are sensitive. In all the composites, the peak stress, strength, and modulus were increased when noticed with the 2D fabric. The experimental results show that the tensile strength of CCK and CCC with carbon fibres used in their weft and warp direction was greater than that of KKC and KKK with Kevlar fibres used in fibres weft and warp direction. The hybridization and 3D orthogonal weaving method also increased the tensile strength. The observation were characterized through scanning electron microscope.

A hybrid algorithm of particle swarm optimization and finite element method to identify local mesoscopic damage of concrete-like materials

Meso-scale material modeling and parameter identification are still unsettled issues in the current multi-scale methods for the field of computational mechanics. In this investigation, a hybrid algorithm of particle swarm optimization and finite element method coupled with continuum damage mechanics is proposed to forecast local mesoscopic elasticity modulus and damage of concrete-like materials based on the macroscopic stress-strain relationship data curve. The algorithm establishes a bridge between mesoscopic mechanical analysis and macroscopic mechanical analysis, which can also guarantee the consistency of analysis in different scales. A representative numerical case is conducted to support the algorithm. Additionally, the effect of different divisions of representative volume element is analyzed based on the algorithm, and the recommended size of representative volume element is 5 mm. The prediction results match well with the corresponding macroscopic experimental results and mesoscopic experimental results based on the chosen recommended size of representative volume element. The effectiveness of the algorithm is verified, which can support an effective numerical tool to optimize and identify mesoscopic mechanical parameters and damage for multi-scale material modeling and analysis.

Biomechanical characterization of normal and pathological human ascending aortic tissues via biaxial testing Experiment, constitutive modeling and finite element analysis

BackgroundAortic dissection and atherosclerosis are two common pathological conditions affecting the aorta. Aortic biomechanics are believed to be closely associated with the pathological development of these diseases. However, the biomechanical environment that predisposes the aortic wall to these pathological conditions remains unclear. MethodsSixteen ascending aortic specimens were harvested from 16 human subjects and further categorized into three groups according to their disease states: aortic dissection group, aortic dissection with accompanied atherosclerosis group and healthy group. Experimental stress-strain data from biaxial tensile testing were used to fit the anisotropic Mooney-Rivlin model to determine material parameters. Computed tomography images or transesophageal echocardiography images were collected to construct computational models to simulate the stress/strain distributions in aortas at the pre-dissection state. Statistical analyses were performed to identify the biomechanical factors to distinguish three groups of aortic tissues. ResultsMaterial parameters of anisotropic Mooney-Rivlin model were fitted with average R2 value 0.9749. The aortic diameter showed no significant difference among three groups. Changes of maximum and average stress values from minimum pressure to maximum pressure (△MaxStress and △AveStress) had significantly difference between dissection group and dissection with accompanied atherosclerosis group (p = 0.0201 and 0.0102). Changes of maximum and average strain values from minimum pressure to maximum pressure (△MaxStrain and △AveStrain) from dissection group were significant different from healthy group (p = 0.0171 and 0.0281). ConclusionChanges of stress and strain values during the cardiac cycle are good biomechanical factors for predicting potential aortic dissection and aortic dissection accompanied with atherosclerosis.

A mechanics-informed deep learning framework for data-driven nonlinear viscoelasticity

A mechanics-informed, data-driven framework for learning the constitutive law of a nonlinear viscoelastic material from stress–strain data using deep artificial neural networks (ANNs) is proposed. In this framework, each ANN architecture is designed and its input and output are selected such that fundamental laws of mechanics and thermodynamics relevant to nonlinear viscoelasticity are strongly satisfied by the resulting data-driven constitutive model. The framework itself extends a previously developed mechanics-informed methodology for the data-driven constitutive modeling of nonlinear elasticity to account for the dependence of the stress on the entire strain history. It is grounded in an additive decomposition of the strain energy density and an internal variable approach to viscoelasticity. Collectively, these are characterized by three potentials whose ANN representations are taught the second law of thermodynamics, various stability conditions, consistency (preservation of rigid body modes), and the recovery of elastic limits. The proposed mechanics-informed deep learning framework for data-driven nonlinear viscoelasticity is illustrated and its performance is assessed for one academic problem where synthetic data is generated by a nonlinear convolution; a coupon-level application associated with a multi-scale homogenization of a viscoelastic woven fabric material; and two representative finite element analyses performed using the material law generated during the previous application, to highlight different features of the framework.

Mechanical Analysis and Constitutive Modeling of Nonlinear Behavior of Silver-based Conductive Ink

Stretchable electronic devices are progressively deployed in many applications of mechanical, electrical, and bio-medical engineering. These circuits are made of stretchable and flexible substrate, as well as conductive ink, and various electronic components. The choice of components and layouts for the substrate and conductive ink can regulate the stretchability of stretchable circuits. On top of that, the substance utilized to create the conductive ink must have high electrical conductivity and strong adherence to the substrate in order to produce a high-quality stretchable printed circuit. Thus, this study focused on the development of stretchable conductive ink using silver powder as a conductive filler and PDMS-OH as a binder. The mechanical properties of the synthesized ink were investigated via simple uniaxial tensile testing method and nanoindentation technique, respectively. Accordingly, the modulus of elasticity, tensile stress and yield stress of the ink were obtained as 5.72 MPa, 1.195 MPa, and 0.86 MPa, congruently at 137% strain before undergoing failure. The experimental stress-strain data was then employed on the elastic-plastic constitutive model to investigate the elastomeric properties of the ink as it is an alternative method of lengthy and expensive procedures of validating different polymers. Moreover, the hardness and reduced modulus of the ink were evaluated by nanoindentation method using 5 mN maximum load with 0.5 mN/s loading/unloading rate and 2 secs holding time. Consequently, the hardness and reduced modulus values were obtained as 1.45 MPa and 34.53 MPa, respectively. These values were further validated by Oliver-Pharr method, and were in a good agreement.

An insight into high-temperature deformation mechanism of magnesium in-situ composite through development of Johnson-Cook and constitutive model

The establishment of deformation mechanisms of Mg-metal matrix composite (Mg-MMC) is important to improve the high-temperature challenging applications. In this present work, an AZ91/TiC + TiB2 hybrid in-situ Mg-MMC was synthesized, and its deformation mechanisms were studied through a uniaxial hot compressive test at different temperatures and strain rates. The Johnson-Cook (JC) model and constitutive equation were established using experimental stress-strain data. Through the development of JC model, it was revealed that the TiC–TiB2 particles enhanced the yield strength parameter and increased the activation energy of the in-situ composite compared to the parent alloy. The load-shifting capability and grain refinement were found to be the dominating mechanisms, which effectively restricted dislocation movement during deformation, resulting in improved deformation resilience of the composite. A detailed study of JC model and constitutive equation parameters was analyzed with a focus on their microstructures.

Rapid hydration and weakening of anhydrite under stress: implications for natural hydration in the Earth's crust and mantle

Abstract. Mineral hydration is an important geological process that influences the rheology and geochemistry of rocks and the fluid budget of the Earth's crust and mantle. Constant-stress differential compaction (CSDC) tests, dry and “wet” tests under confining pressure, and axial-stress tests were conducted for the first time to investigate the influence of triaxial stress on hydration in anhydrite–gypsum aggregates. Characterization of the samples before and after triaxial experiments was performed with optical and scanning electron microscopy, including energy-dispersive spectroscopy and electron backscatter diffraction mapping. Stress–strain data reveal that samples that underwent constant-stress differential compaction in the presence of fluids are ∼ 14 % to ∼ 41 % weaker than samples deformed under wet conditions. The microstructural analysis shows that there is a strong temporal and spatial connection between the geometry, distribution, and evolution of fractures and hydration products. The increasing reaction surface area in combination with pre-existing gypsum in a gypsum-bearing anhydrite rock led to rapid gypsification. The crystallographic orientations of newly formed vein gypsum have a systematic preferred orientation for long distances along veins, beyond the grain boundaries of wall-rock anhydrite. Gypsum crystallographic orientations in {100} and {010} are systematically and preferentially aligned parallel to the direction of maximum shear stress (45∘ to σ1). Gypsum is also not always topotactically linked to the wall-rock anhydrite in the immediate vicinity. This study proposes that the selective inheritance of crystal orientations from favourably oriented wall-rock anhydrite grains for the minimization of free energy for nucleation under stress leads to the systematic preferred orientation of large, new gypsum grains. A sequence is suggested for hydration under stress that requires the development of fractures accompanied by localized hydration. Hydration along fractures with a range of apertures up to 120 µm occurred in under 6 h. Once formed, gypsum-filled veins represent weak surfaces and are the locations of further shear fracturing, brecciation, and eventual brittle failure. These findings imply that non-hydrostatic stress has a significant influence on hydration rates and subsequent mechanical strength of rocks. This phenomenon is applicable across a wide range of geological environments in the Earth's crust and upper mantle.

Interpretation of uniaxial, confined compression test data for agricultural topsoils

Traditionally, soil strength is estimated from uniaxial, confined compression tests by procedures adopted from classical soil mechanics. The heterogeneity of agricultural topsoil calls for an alternative approach. Undisturbed soil cores were collected in the plough layer of 14 soils in arable agriculture. Soil texture ranged from coarse sandy to silty loam soils with a maximum of 20% clay. The samples were drained to either of six matric potentials in the range from − 30 to − 300 hPa. Uniaxial, confined compression was applied to ∼800 kPa with strain-controlled stress application (1 mm min−1). Measured strain was fitted to stress by the Morgan-Mercer-Flodin (MMF) model. The model fitted data remarkably well for all samples. Three fitting parameters of the model reflected physical characteristics of soil reaction to stress. The estimates of soil compressibility calculated from the model at 10 kPa (C10) correlated closely and linearly to the Cs index considered to reflect elastic deformation in classical studies of soil compression tests. Soil bulk density and content of soil organic matter decreased C10 as well as compressibility at 100 (C100) and 400 kPa (C400). A complex pattern in the effects of soil texture and soil moisture on compressibility was revealed. The pattern in strain-stress data is interpreted as a reflection of a gradual transition from elastic to plastic deformation of the mixture of structural units. The MMF model is suggested for interpretation of strain-stress data from uniaxial, confined compression tests. This implies use of stress in a linear scale.

The Influence of Crystallographic Orientation and Grain Boundary on Nanoindentation Behavior of Inconel 718 Superalloy Based on Crystal Plasticity Theory

The crystal plasticity finite element method (CPFEM) is widely used to explore the microscopic mechanical behavior of materials and understand the deformation mechanism at the grain-level. However, few CPFEM simulation studies have been carried out to analyze the nanoindentation deformation mechanism of polycrystalline materials at the microscale level. In this study, a three-dimensional CPFEM-based nanoindentation simulation is performed on an Inconel 718 polycrystalline material to examine the influence of different crystallographic parameters on nanoindentation behavior. A representative volume element model is developed to calibrate the crystal plastic constitutive parameters by comparing the stress-strain data with the experimental results. The indentation force-displacement curves, stress distributions, and pile-up patterns are obtained by CPFEM simulation. The results show that the crystallographic orientation and grain boundary have little influence on the force-displacement curves of the nanoindentation, but significantly influence the local stress distributions and shape of the pile-up patterns. As the difference in crystallographic orientation between grains increases, changes in the pile-up patterns and stress distributions caused by this effect become more significant. In addition, the simulation results reveal that the existence of grain boundaries affects the continuity of the stress distribution. The obstruction on the continuity of stress distribution increases as the grain boundary angle increases. This research demonstrates that the proposed CPFEM model can well describe the microscopic compressive deformation behaviors of Inconel 718 under nanoindentation.

New aspects of a single-crystal gradient plasticity model: Rate-dependency of size-dependent response

Gradient crystal plasticity and rate-dependent plasticity models have been widely developed. However, describing the rate-dependency of the size-dependent behavior remains a long-term challenge and is of great interest in the field. This study investigates the interaction between the rate and size dependency of single crystals. The main contribution is to determine whether the size dependency of the stress–strain responses increases or decreases with increasing deformation rates. A thermodynamically consistent model based on the finite-deformation single-crystal gradient plasticity framework proposed by Gurtin is presented. In the current formulation, the particular features are a rate-dependent function and a rate-sensitivity parameter incorporated into the dissipative gradient strengthening term. These features allowed us to observe the disparate rate-dependencies induced by the dissipative conventional and dissipative gradient terms. From an experimental perspective, few studies have investigated the interaction between the size- and rate-dependence of single crystals. Interestingly, these studies reported different modes of interaction. Here, we categorize existing experimental stress–strain data into two distinct groups: first, the stress data obtained at fixed overall strains, and second, those captured at offset strains, that is, at the yield or post-yield strains. The numerical results obtained through a two-dimensional framework and based on a common set of material and modeling parameters were qualitatively compared with existing experimental data reported for different materials. Trends in the interactions were numerically captured and discussed. The results indicate the promising potential of the model for describing the rate-dependency of the size-dependent yield stress and subsequent behaviors.

Experimental study on the post-fire cyclic behavior of Q960E ultra-high-strength structural steel

This paper presents an experimental study on the cyclic behavior of Q960E ultra-high-strength steel (UHSS) after exposure to elevated temperatures and subsequent cooling down by water. The test program comprised six temperature levels ranging from room temperature to 900 °C, along with four cyclic loading protocols. A total of 46 tests were conducted in this study, and the failure mode, hysteretic curve, springback behavior, Young’s modulus, and fracture strain were discussed in detail. Subsequently, a method was proposed to calibrate the equivalent strain–stress data and true strain–stress data based on the reversion method with axisymmetric model. Based on the calibrated data, the stress–strain relationship and strain hardening behavior were examined, and the corresponding parameters were also calibrated. Finally, comparisons of the numerical simulation results and experimental data demonstrated that the suggested constitutive model accurately described the cyclic behavior of Q960E UHSS after elevated temperatures. The findings of this study have potential applications in evaluating the seismic performance of UHSS structures following exposure to fire.

The influence of climatic factors on the sublimation and mechanical properties of paper fiber reinforced ice as building envelope

The climatic adaptability of ice-shell architecture under long-term natural influence remains underexplored. This study investigates the weatherability of paper fiber reinforced ice (PFRI) as envelopes, including the changes in the sublimation mechanism and mechanical properties changes. The PFRI specimens were layered poured and exposed to nature. The sublimation rates, climatic parameters, and stress–strain data were recorded. The results suggest that PFRI sublimation is a dynamic process with cumulative effects. A calculation model is proposed to predict sublimation in engineering. Considering fibre escape, PFRI with 2% or 3% fibre content has better weatherability, with a 30% decrease in elastic modulus on the sunny side and a 15% decrease on the shaded side.

Thermomechanical Modeling of Material Flow and Weld Quality in the Friction Stir Welding of High-Density Polyethylene.

A thermomechanical model of the friction stir welding (FSW) of high-density polyethylene (HDPE) was developed by incorporating a Coupled Eulerian-Lagrangian (CEL) approach. A Johnson Cook (JC) material model of HDPE was developed through experimentally generated strain-rate- and temperature-dependent stress strain data. Two sets of FSW process parameters with minimum and maximum weld defects were numerically modeled. The numerically calculated temperature distribution, material flow and flash and potential defects were validated and discussed with the experimental results. Tracer particles allowed to visualize the material movement during and after the tool had traversed from the specified region of the workpiece. Both numerical models presented similar maximum temperatures on the upper surface of the workpiece, while the model with high traverse speed and slow rotational speed had narrower shoulder- and heat-affected zones than the slow traverse, high rotational speed model. This contributed to the lack of material flow, hence the development of voids and worm holes in the high traverse speed model. Flash and weld defects were observed in models for both sets of process parameters. However, slow traverse, high rotational speeds exhibited smaller and lesser weld defects than high traverse, slow rotational speeds. The numerical results based on the CEL approach and JC material model were found to be in good agreement with the experimental results.

Toward Patient-specific Pessary to Manage Pelvic Organ Prolapse: Design and Simulation.

This study proposed a novel design and personalized approach to developing an intra-vaginal device, also known as a pessary, for the treatment of Pelvic Organ Prolapse (POP). Although POP is likely to have a more diverse dynamic than other health conditions in women, it is currently treated as a "one-shape-fits-all" problem in all cases. Pessaries are conservative devices inserted into the vagina to support its internal structure and predominantly come in a ring shape design. Failure rates as high as 50% within the first year of use have been attributed to the poor design of these pessaries; with symptoms such as irritation, bleeding, and lacerations felt by most users. To address this problem, a new base shape design was proposed and its deformation was examined using Finite Element Analysis (FEA). Based on the anatomical measurements of each patient, the base design can be adjusted accordingly. To demonstrate the effectiveness of the proposed design, a comparative study was conducted with the most commonly used support pessary, also known as the ring pessary. In order to model the large deformation of the pessaries, the hyperelastic constitutive law (Yeoh model) was fitted to the available stress-strain data of SIL 30 (a silicone urethane resin supplied by Carbon Inc.). The results showed that re-directing the reaction forces of the pessary towards the lateral walls, supported by the pelvic bones, could decrease the overall displacement of the pessaries, and provide effective symptomatic relief thereby, delaying or preventing surgical procedures.Clinical relevance- There is a clear clinical need to develop a more effective conservative therapy for managing POP. The personalized pessaries proposed in this paper can be an effective method for providing symptomatic relief and avoiding displacement, compared to the currently available devices on the market. Made-to-measure for each patient, the devices are anatomically suited and can be adjusted throughout a patient's treatment plan to allow for higher compliance and overall success rate.

Dynamic Compression Simulation of Magnetorheological Elastomer Using Bouc-Wen Hysteretic Model

This paper explores the versatility of Bouc-Wen hysteresis model in simulating the dynamic behaviour of magnetorheological elastomer (MRE) material. Bouc-Wen model have been used in many field of science including modelling the hysteresis phenomenon happen in magnetic material, elastomer, base isolation of structures and many more. Introduced by the Robert Bouc, this nonlinear hysteretic model has been modified by many researchers to suit different applications. Compression testing of MRE material under high strain amplitude produces nonlinear hysteresis curve based on stress-strain data. Bouc-Wen hysteretic model has been found to be able to simulate the hysteresis curve of MRE material using parameter identification method within MATLAB Simulink.

Dynamic mechanical properties and constitutive model of photosensitive resin specimens at different temperatures

In order to reveal the dynamic mechanical properties of resin-molded parts prepared from photosensitive resin composition at different temperatures, four typical service temperatures (26 °C, 50 °C, 70 °C and 90 °C) were selected, and the mechanical properties of photosensitive resin specimens under quasi-static and high strain rate (1200 s−1, 1500 s−1 and 1800 s−1) loading were tested by universal material testing machine and split Hopkinson pressure bar (SHPB) experimental device. The stress–strain data of the material were obtained. Results show that the stress of photosensitive resin specimens decreases with the increase of temperature under quasi-static and high strain rate loading conditions, reflecting a certain temperature softening effect. Two typical stages of strain softening and strain hardening exist in the quasi-static compression process of the specimens at room temperature, while the specimens only exhibit strain hardening at 50 °C, 70 °C and 90 °C. Under dynamic loading, the elastic modulus, peak stress and peak strain of the photosensitive resin increase with the increase of the strain rate, reflecting an obvious effect of strain rate strengthening. The nonlinear thermo-viscoelastic constitutive model can better describe the mechanical behavior of the material under high strain rates and service temperatures, and the experimental values are in good agreement with the fitted values of the model. The results can provide theoretical model and method support for the design and development of resin-based materials and the optimization of their mechanical properties.

Analysing the effect of defects on stress concentration and fatigue life of L-PBF AlSi10Mg alloy using finite element modelling

Additive manufacturing (AM) is a developing manufacturing technology, which provides excellent attributes compared to other manufacturing techniques. However, one of the critical challenges is the presence of defects that hinder the mechanical properties of the parts, particularly the fatigue life. Experimental understanding of fatigue is a cumbersome process. Therefore, numerical prediction based on specified conditions (such as porosity and applied load) can be an alternative to experimental analysis at the design stage of AM parts. In this study, elastic–plastic finite element analysis (FEA) is performed to obtain the stress distribution around pores, and their resultant effect on fatigue life for L-PBF (laser powder bed fusion) produced AlSi10Mg alloy samples. The stress field is calculated for both single and multiple pore models, where stress concentration is evaluated as a function of the pore’s location and its size. It is found that both pore location and size affect the stress field; however, location effects dominate over pore size. For the same remote applied stress level, the stress concentration around the pore increases with an increase in pore size, and the local maximum stress occurs near the pores that are closest to the surface. The current study also evaluates the relative effect of porosity fraction, average pore size, and location. It is found that the magnitude and sensitivity of stress concentration are hierarchically controlled by porosity location, pore size, and porosity density. A multi-scale finite element (FE) model is proposed based on inherent porosity data measured using Computed Tomography (CT) to predict overall fatigue life. The fatigue cycles are calculated using the rainflow counting algorithm in FE Safe using the stress–strain data obtained from the proposed FEA model. Using the proposed model, it is possible to generate S–N curves for any loading condition for a given porosity condition (porosity density and average pore size). The S–N curve results obtained from the FE model are compared to the experimental observations. The predicted fatigue life shows approximately 5% error with experimental results at high stress loading conditions. However, the proposed model overpredicts the fatigue life at low stress loading by almost 30%.

Impact of the plasticity modeling on fatigue life prediction for steels showing modest non-proportional hardening

This study evaluated the influence of Tanaka parameter-based cyclic plasticity modeling on fatigue life estimation under multiaxial loading. The life predictions based on the experimental stress–strain data, simulated by the Chaboche cyclic plasticity model and Chaboche model with the implemented Tanaka parameter, were compared for this purpose. The fatigue life was then calculated using three popular prediction models for the two steel grades exhibiting moderate non-proportional hardening. Eleven multiaxial loadings were investigated, including proportional, 90° out-of-phase, and asynchronous cases. Modeling the cyclic material response using the coupled Chaboche and Tanaka models revealed to have improved all fatigue life predictions.

Nanoindentation study of δ-phase zirconium hydride using the crystal plasticity model

Zirconium hydride precipitation degrades the fracture toughness of nuclear reactor fuel cladding tube. Due to the difficulty of experiment, deep understanding on mechanical properties of zirconium hydride via numerical approaches is in a great need. To study the mechanical properties of zirconium hydride, the crystal plasticity finite element model considering geometrically necessary dislocations evolution is used to simulate the nanoindentation deformation behavior of single-crystal δ-hydride. The parameters in the crystal plasticity model are calibrated by Young's modulus along different crystallographic orientations and experimental stress-strain data at different strain rates. The predicted polycrystalline Young's modulus, Poisson's ratio, and nanoindentation hardness are in good agreement with the experimental results. The simulation results show that the nanoindentation hardness strongly depends on the indentation depth when it is smaller than 500 nm. Furthermore, the effects of crystallographic orientation and zirconium matrix on the indentation results are also studied. We find that the nanoindentation hardness of δ-hydride is slightly orientation dependent. For smaller hydride size or larger indentation depth, the surrounding zirconium matrix undergoes plastic deformation, which leads to a significant underestimate of the nanoindentation hardness of the hydride.

Simple inverse FEM based procedure of flow curve extraction applied to unirradiated and irradiated 73 W weld material

The H2020 FRACTESUS project is aimed to validate miniaturized compact tension specimens usage for fracture toughness characterization of irradiated materials. One of the tasks in the project is devoted to the numerical simulations of the 0.16T and 1T-CT specimens and comparison of their stress/strain fields in. For this purpose accurate material flow curves are necessary to derive comparable mechanical response between the numerical models and experiments. This paper presents a simple technique of flow curve extraction from the tensile test using engineering stress–strain data. The proposed method utilizes a coarse meshed Finite Element Model and a manual flow curve data optimization procedure without additional scripting. The robustness of the method was shown on the example of the 73 W weld material in the unirradiated and irradiated states, tested at various temperatures from −100 °C to 125 °C. The obtained numerical flow curves are in a very good agreement with the experimental results. Moreover, the advantages of the proposed method were shown over either the methods based on extrapolation of the predictions of popular models with parameters fitted to prior necking or the method based on fracture diameter measurements. The final validation of the proposed methodology was demonstrated by numerical simulations of fracture toughness tests on precracked Charpy specimens.