Hardening Material Model Research Articles

Experimental and numerical investigation of material non-linearity in steel elements under different loading protocols

In order to investigate the behaviour of a steel structure and provide effective design, most of the time analyses procedures which can take account the non-linear material behaviour are needed. These non-linear analysis procedures which are widely applied with different levels of accuracy, adopt two major approaches which can be classified as lumped plasticity and distributed plasticity models. This paper aims to analyze the accuracy of two different plasticity approaches such as lumped and distributed plasticity models on providing the non-linear material behaviour of steel elements under different loading protocols by comparing numerical and experimental results. In the first part, monotonic and cyclic quasi static tests and pseudo dynamic tests under instantaneous constant load and seismic load are conducted by using the small scale Load and Boundary Condition Box. Small scale steel specimens are used for the experiments. Results of the experiments are comprehensively reported. In the second part of the study, several numerical models are generated for each test. Monotonic and cyclic loading pushover analyses are carried out with both lumped plasticity models and distributed plasticity models. In these numerical studies, different types of material models are considered and numerical analysis results are validated against the experimental results. Accuracy of lumped plasticity and distributed plasticity models are assessed and a comprehensive comparison of different analysis and material models is reported. It is generally observed that using the fiber based method with bilinear kinematic hardening material model provides more accurate element responses for hot rolled steels.

Helical Extrusion Process of General Polygonal Section Shapes through Curved Dies

Practically, the helical products used as a mechanical part to satisfy the needs of mechanical strength and artistic appearance. In addition, during recent 5 years it used to produce an ultra-fine grain metal structure. However, there are very little works regarding this type of extrusion so far. This work proposed a new formulation for helical deformation zone to produce general helical polygonal shapes through a streamlined die that are usually made by hot extrusion through taper die. The general die surface was represented analytically. The velocity and strain rate fields are derived depending on the volume constancy and the velocity boundary conditions. The upper bound forming pressure was obtained for various frictional conditions, area reduction, helix angle, and die length. The results show that the axis of the product does not rotate through the helical extrusion. The peak value of the strain rate is located close to the die outlet and decreases as the helix angle increases. The optimum die length becomes high as the helix angle increases. The forming pressure increases with increasing helix angle, area reduction, factor of friction, while decreases when the number of sides increases. The theoretical results were verified with previous work of zero twist and showed completely compatible. A finite element solution was done using hardening material model to verify the analytical results and metal flow and to examine the strain and stress fields in the product.

Analytical Solution of the Pipe Burst Pressure Using Bilinear Stress-Strain Model and Influence of Corrosion Defects on it

This article presents the derivation of analytical solution of the burst pressure of cylindrical vessel with hardening material model. The material model is considered a bilinear model for stress-strain intensity. Solution is based on the constant volume theorem for plastic strain process. Derived analytical equations have been verified by experimental measurement on pipe models in laboratory and also by the numerical modeling using the Finite Element Method. The experimental results are in good compliance with analytical solution. The effect of corrosion defect on the burst pressure is also modeled.

A new semi-analytical approach for obtaining crack-tip stress distributions under variable-amplitude loading

Near threshold fatigue crack response is extremely sensitive to load history. It is associated with the influence of near-tip stress on instantaneous resistance of crack tip surface layers to failure under atmospheric conditions. The paper deals with computational aspects of stress and strain distributions at the crack tip. A new approach is proposed to obtain near-tip stress under variable amplitude loading. The method considers a combination of standard rules for determining local strains (Linear rule, Neuber rule, ESED method, etc.) and well-known in Finite Element Analysis (FEA) return mapping algorithm in context of nonlinear mixed hardening material model. Iterative procedure based on Newton-Raphson method is proposed to calculate plastic variables and near-tip stress at each load step. The calculated results obtained by new model are validated with the traditional approach in case of Al2024-T3 alloy for constant amplitude loading after tensile/comprehensive overloads.

Elastic-Plastic Analysis Under Proportional and Non-Proportional Loading Paths Using Deformation Plasticity Theory

An estimation of elastic-plastic stresses and strains is presented for mechanical components, using pseudo elastic analysis based on the deformation theory of plasticity. Analysis of two applications, one under proportional loading and other under non-proportional loading paths using pseudo elastic finite element method, is presented. A rectangular plate with a hole under tension loading and a rectangular plate fixed at one end under bending-tension non-proportional loading are considered for analysis. Pseudo Elastic finite element analysis for proportional loading uses elastic solutions and varies material properties for elements in plastic zone to estimate elastic-plastic solution. A finite element code is developed based on pseudo elastic analysis method. An attempt is made to extend pseudo elastic analysis to analyze bending-tension non-proportional loading problem. Both applications in consideration are assumed to be of Von Mises material and follow isotropic hardening rule with elastic-linear hardening material model. Non-linear analysis of the plate with a hole under proportional tensile loading and that of rectangular plate under bending-tension non-proportional loading are performed in ANSYS and results are compared for validation and are observed to be in good agreement with present analysis.

A non-associated anisotropic plasticity model with mixed isotropic–kinematic hardening for finite element simulation of incremental sheet metal forming process

This paper focuses on numerical simulation of single point incremental forming (SPIF) process. Via a user-defined material (VUMAT) subroutine is employed to implement a non-associated mixed isotropic–kinematic hardening material model. The accuracy of the proposed non-associated flow rule model to predict the material behavior and the anisotropy in sheet metal forming simulations is examined by comparing numerical results with experimental measurements. The suggested model shows good agreement with experimental results compared to the associated Hill_R and Hill_S models. The proposed non-associated flow rule demonstrates a good efficiency to simulate the springback after sheet metal forming and to predict the thickness variation during incremental sheet metal forming process. The present non-associated model can improve the prediction of both anisotropic and hardening behaviors of material used in numerically controlled sheet metal forming technology.

A novel analytical model for straightening process of rectangle-section metal bars considering asymmetrical hardening features

The applied straightening moment and the springback after unloading with respect to the straightening process of rectangle-section metal bars have a direct influence on the straightening accuracy and efficiency. In this article, an asymmetrical hardening material model is first proposed to describe the stress–strain curves considering the asymmetrical features of yield stress and plastic hardening stage in tension and compression, and it is also compared with the traditional linear hardening material model. To accurately evaluate the elasto-plastic bending deformation and the springback in the straightening process, an analytical model for the loading and unloading moments is then established. The strain and stress distributions in elastic and plastic regions during the straightening process are also discussed in this article. Finally, the straightening experiments of rectangle-section metal bars under different heat-treated conditions are conducted on the ROSE-JZ50 straightening machine with displacement sensors, force sensors and strain gauges to validate the proposed analytical straightening model.

Application of multi-phase viscoplastic material modelling to computational welding mechanics of grade-s960ql steel

The sound numerical prediction of welding-induced thermal stresses, residual stresses, and distortions strongly depends on the accurate description of a welded material's thermomechanical deformation behaviour. In this work, we provide experimental data on the viscoplastic deformation behaviour of a grade-s960ql steel up to a temperature of 1000C∘. In addition, a multi-phase viscoplastic material model is proposed, which accounts for the experimentally observed isothermal deformation behaviour of grade-s960ql steel base and austenitised material, as well as for athermal contributions that originate from solid-state phase transformations. The multi-phase viscoplastic and a classic rate-independent isotropic hardening material model were applied in the numerical simulations of both-ends-fixed bar Satoh tests and a single-pass gas metal arc weld. The influence of material modelling choices on the agreement between numerical simulation and experimental results is discussed, and recommendations for further work are given.

Numerical Modeling and Analytical Investigation of Autofrettage Process on the Fluid End Module of Fracture Pumps

One of the most important components in the hydraulic fracturing is a type of positive-displacement-reciprocating-pumps known as a fracture pump. The fluid end module of the pump is prone to failure due to unconventional drilling impacts of the fracking. The basis of the fluid end module can be attributed to cross bores. Stress concentration locations appear at the bores intersections and as a result of cyclic pressures failures occur. Autofrettage is one of the common technologies to enhance the fatigue resistance of the fluid end module through imposing the compressive residual stresses. However, evaluating the stress–strain evolution during the autofrettage and approximating the residual stresses are vital factors. Fluid end module geometry is complex and there is no straightforward analytical solution for prediction of the residual stresses induced by autofrettage. Finite element analysis (FEA) can be applied to simulate the autofrettage and investigate the stress–strain evolution and residual stress fields. Therefore, a nonlinear kinematic hardening material model was developed and calibrated to simulate the autofrettage process on a typical commercial triplex fluid end module. Moreover, the results were compared to a linear kinematic hardening model and a 6–12% difference between two models was observed for compressive residual hoop stress at different cross bore corners. However, implementing nonlinear FEA for solving the complicated problems is computationally expensive and time-consuming. Thus, the comparison between nonlinear FEA and a proposed analytical formula based on the notch strain analysis for a cross bore was performed and the accuracy of the analytical model was evaluated.

The continuous strength method for the design of high strength steel tubular sections in compression

This paper aims to extend the deformation-based design method named continuous strength method (CSM) for the design of high strength steel tubular sections in compression. The CSM employs a base curve relating the cross-section resistance to its deformation capacity and adopts an elastic, linear hardening material model. Non-slender and slender circular hollow sections (CHS), elliptical hollow sections (EHS), square hollow sections (SHS) and rectangular hollow sections (RHS) were investigated in this study. Hot-finished, cold-formed and built-up steel tubular sections with yield stresses up to 1405 MPa were covered. An extensive numerical study was carried out to supplement the limited test results of high strength steel stub columns in the literature. The cross-section resistances obtained from the proposed CSM, the direct strength method (DSM), and design methods in EN 1993-1-5, EN 1993-1-6, ANSI/AISC 360-10 and AISI S100 were compared with the experimental and numerical capacities of 742 stub columns. It is shown that the proposed CSM can produce more accurate and less scattered strength predictions than the current DSM and design codes.

The continuous strength method for the design of hot-rolled steel cross-sections

The continuous strength method (CSM) is a deformation-based structural design approach that enables material strain hardening properties to be exploited, thus resulting in more accurate and consistent capacity predictions. To date, the CSM has featured an elastic, linear hardening material model and has been applied to cold-formed steel, stainless steel and aluminium. However, owing to the existence of a yield plateau in its stress-strain response, this model is not well suited to hot-rolled carbon steel. Thus, a tri-linear material model, which can closely represent the stress-strain response of hot-rolled carbon steel, is introduced and incorporated into the CSM design framework. Maintaining the basic design philosophy of the existing CSM, new cross-section resistance expressions are derived for a range of hot-rolled steel structural section types subjected to compression and bending. The design provisions of EN 1993-1-1 and the proposed CSM are compared with experimental results collected from the literature and numerical simulations performed in this paper. Overall, the CSM is found to offer more accurate and consistent predictions than the current design provisions of EN 1993-1-1. Finally, statistical analyses are carried out to assess the reliability level of the two different design methods according to EN 1990 (2002).

Finite element simulation of scratch on polypropylene panels

Scratch simulation of polymeric materials has been a challenging task. It requires a material constitutive model that is capable of representing the complicated material response at large strains, and also a modelling method that can comprehensively resolve several physics, i.e., tribology, material deformation and damage, indenter statics and dynamics. This paper discussed the use of two finite element simulation approaches: (i) Abaqus/Explicit Arbitrary Lagrangian-Eulerian (ALE) adaptive meshing and (ii) the Coupled Eulerian-Lagrangian (CEL), in modelling scratches of talc-filled polypropylene using an elastic-plastic with isotropic hardening material model and a hyperelastic-viscoelastic model. The models were evaluated with scratch experiments and a very good agreement between the simulations and experiments was found. Various technical challenges in modelling scratch of polymeric materials were discussed and solved during the development of both successful methods and their merits and drawbacks were also discussed in detail.

Dynamic crushing of cellular claddings with temperature gradient

Considering the applications of cellular materials in the sacrificial claddings for impact/blast alleviation, this study presents a method for the design of cellular foam claddings with temperature gradient under high initial velocity impacts. A one-dimensional model for the compaction of cellular foam claddings with temperature gradient is developed for the striker-rod impact scenario based on a rate-independent, rigid, perfectly plastic, locking (R-P-P-L) idealization of the quasi-static stress–strain curves for aluminum foams. The predictions of the proposed model are compared with FE simulations with the realistic rigid, power-law hardening (R-PLH) material model based on the actual experimentally derived stress–strain curves. The predictions of the dependency of critical length, critical impact velocity and impact force of the cellular foam rod with temperature gradient on the temperature distribution and the relation of critical impact velocity of an aluminum foam rod with a given length to the temperature contrast at its two ends are compared well with the numerical simulations results.

The NeT Task Group 4 residual stress measurement and analysis round robin on a three-pass slot-welded plate specimen

Accurate prediction and measurement of residual stresses in welds is an important part of assuring their short and long-term structural performance in high value, safety critical engineering components and structures. However, both measurements and predictions of weld residual stresses often exhibit high levels of variability that are not widely appreciated. The mission of the European Network on Neutron Techniques Standardization for Structural Integrity (NeT) is to develop experimental and numerical techniques and standards for the reliable characterisation of residual stresses in structural welds.The NeT Task Group 4 project examined residual stresses in a three-pass slot-welded plate specimen fabricated from AISI 316L(N) austenitic stainless steel plate. Several nominally identical specimens were fabricated under closely controlled conditions, with detailed records kept of the manufacturing history, weld process parameters, transient temperatures during welding, and the resulting geometric distortions. Comprehensive stress-strain material property characterisation was then undertaken, extending to the isothermal cyclic tests necessary to calibrate the mixed isotropic-kinematic material hardening models required for accurate weld residual stress prediction. Parallel residual stress measurement and simulation round robins were performed by a large number of participants from around the world.Residual stresses were measured using neutron and high energy synchrotron diffraction, surface X-ray diffraction, surface and deep hole drilling, the contour method, and ultrasonics. Neutron diffraction measurements were made at eight different instruments. The diffraction measurements database alone is large enough to generate reliable mean profiles, to identify clear outliers, and to establish that there is no statistically significant difference in the residual stress field in the specimens used for the non-destructive measurements. NeT Task Group 4 gives a unique insight into the real-world variability of diffraction-based residual stress measurements, and forms a reliable foundation against which to benchmark other measurement methods.NeT Task Group 4 is also a unique test bed for the development and validation of weld residual stress simulation techniques in austenitic stainless steel. Its combination of extensive materials characterisation, accurately characterized welding temperature transients, and reliable residual stress and distortion measurements is currently unrivalled. About thirty finite element simulations were submitted to the network over the course of the project, giving insights into the required accuracy of welding thermal solutions, the mechanical solution accuracy achievable using optimized material constitutive models, and the level of acceptable error in finite element residual stress simulation results for use in structural integrity assessments of high integrity engineering components.

A New Approach Towards Life Prediction of Case Hardened Bearing Steels Subjected to Rolling Contact Fatigue

Abstract The failure of a bearing-raceway assembly is governed by the spatial distribution of subsurface stresses at the vicinity of a bearing-raceway contact and the evolution of these stresses during rolling contact fatigue (RCF) loading. In this paper, we propose an experimental methodology that allows one to accurately measure the location and magnitude of the cyclically evolving elastoplastic von Mises stresses in terms of microhardness numbers. An M50NiL steel rod is subjected to RCF by three silicon nitride (Si3N4) balls for over several hundred million cycles at 5.5 GPa contact stress level. Microindentation hardness measurements within the subsurface RCF-affected regions of the rod revealed significant material hardening. A mechanistic methodology to construct a stress-life (S-N) diagram for RCF loading is proposed. S-N diagrams are constructed based on maximum von Mises stress amplitude and volume average von Mises stress amplitude. The effects of elastic modulus and yield strength gradient on stress fields are also considered in this analysis. Comparison of S-N diagrams based on both stress amplitudes indicates that the maximum von Mises stress amplitude overpredicts the fatigue strength of material in S-N diagrams. The experimental results obtained by following this methodology can help construct material hardening models for RCF, which may lead to an improved estimate of bearing fatigue life.

Numerical simulation of the roll levelling of third generation fortiform 1050 steel using a nonlinear combined hardening material model

The roll levelling is a flattening process used to remove the residual stresses and imperfections of metal strips by means of plastic deformations. During the process, the metal sheet is subjected to cyclic tension-compression deformations leading to a flat product. The process is especially important to avoid final geometrical errors when coils are cold formed or when thick plates are cut by laser. In the last years, and due to the appearance of high strength materials such as Ultra High Strength Steels, machine design engineers are demanding reliable tools for the dimensioning of the levelling facilities. Like in other metal forming fields, finite element analysis seems to be the most widely used solution to understand the occurring phenomena and to calculate the processing loads. In this paper, the roll levelling process of the third generation Fortiform 1050 steel is numerically analysed. The process has been studied using the MSC MARC software and two different material laws. A pure isotropic hardening law has been used and set as the baseline study. In the second part, tension-compression tests have been carried out to analyse the cyclic behaviour of the steel. With the obtained data, a new material model using a combined isotropic-kinematic hardening formulation has been fitted. Finally, the influence of the material model in the numerical results has been analysed by comparing a pure isotropic model and the later combined mixed hardening model.

Strain-based critical plane approach to predict the fatigue life of high frequency mechanical impact (HFMI)-treated welded joints depending on the material condition

After post-treatment with high frequency impact treatment (HFMI) of weld toes, a significant increase of fatigue strength or fatigue life can be achieved. Due to the lack of methods for the quantitative prediction of the HFMI benefits depending on the process and treated material, a widespread use of this process has not yet happened. One reason for that issue is that at the moment, no methods exist to predict the influence of the HFMI-treatment on welded components and structures at the moment in advance depending on the HFMI-treatment parameters. For this case, a strain-based approach based on the finite element (FE) simulation of the HFMI-process and the subsequent evaluation by critical plane approaches of the FE-post-processing was developed. This approach principally considers the beneficial effects of compressive residual stresses, notch effect reduction, and hardening of the HFMI-treated surface layer. Furthermore, residual stress relaxation during fatigue loading was taken into account. For numerical prediction of the influence of HFMI-treatment of welds, process parameters at the real device were measured and a suitable material hardening model was used from previous work to describe the conditions in the surface layer. After this, the process chain of welding, HFMI-treatment, and fatigue loading of butt joint specimen were simulated. The estimated fatigue life values were compared with the values of the fatigue tests for two different treatment intensities and also a good agreement was reached.

Evaluation of Spalling Fallout on Excavation Disturbed Zone under Deep Hard Rock Tunnel

The prediction of compressive stress-induced failures is of concern when designing and constructing facilities in rock for deep underground excavation. The purpose of this study is to model compressive stress-induced failure and fallouts with appropriate material models and strength parameters for deep hard rock tunnel excavation. Three method of numerical modelling are used, which are Generalised Hoek-Brown; Mohr-Coulomb; and Mohr-Coulomb with Cohesion Softening Friction Hardening (CSFH) material models for capturing the observed rock behaviour. A parametric study was also carried out to verify that the peak friction angle of 10° used in CSFH model. The results show that numerical models used only Generalised Hoek-Brown and Mohr Coulomb strength parameters does not show a good agreement with the observed fallout. The comparison revealed that the numerical models using the Mohr-Coulomb with CSFH provides most realistic to the observation fallout length. This model is valid for prediction of failure and fallouts in hard rock masses with high quality (GSI >65 MPa; intact rock compressive strength >70MPa).

Effects of spall edge profiles on the edge plastic deformation for a roller bearing

A clear understanding of the plastic deformations at the spall edges is a primary task for the edge propagation predictions in rolling element bearings. This work proposed an elastic–plastic two-dimensional finite element model for calculating the contact stress and plastic deformation between the rolling element and raceway. This model includes a rolling element and one raceway. The rectangular plane strain solid elements are used to formulate the finite element model. The Coulomb model is used to formulate the friction force between the rolling element and raceway. A bilinear kinematic hardening material model is used in the finite element model, which can formulate the elastic–plastic deformations. The studied spall edge profiles are assumed to be sharp and cylindrical ones. To validate the finite element model, the contact deformations between the rolling element and the raceway from the proposed model and Hertzian contact theory are compared. Effects of spall edge profiles on the edge plastic deformations at the edge are analyzed, as well as the edge plastic deformation zone width. Based on the numerical results, the relationship between the edge plastic deformation and the spall edge profile, and that between the edge plastic deformation zone width and the spall edge profile are established. The results show that the edge plastic deformation is significantly influenced by the spall edge profiles, as well as the edge plastic deformation zone width. This paper provides a clear understanding of the effects of the edge profiles on the plastic deformations and propagation at the spall edge.

Modeling the Cycle-Dependent Material Hardening Behavior of 508 low Alloy Steel

Chaboche-based material hardening models were used to investigate the cycle/time dependency of the elastic-plastic behavior of 508 low alloy steel (LAS), a commonly used material for light water reactor components. Strain-versus-stress curves were derived from uniaxial tensile and fatigue experiments conducted under various conditions, such as in-air at room temperature, in-air at 300 °C, and primary loop water conditions for a pressurized water reactor (PWR). These data were then used to estimate material parameters such as the elastic modulus, yield stress, and variables related to Chaboche-based linear and nonlinear kinematic hardening models. The results estimated from the fatigue test data suggest that the material behavior is highly sensitive to fatigue cycles, in addition to temperature. The authors anticipate that the findings of this research will help develop computer-based advanced modeling tools to extrapolate stress-strain evolution of reactor components under multi-axial stress states and, hence, will help predict their fatigue life more accurately.