Hardening Law Research Articles

On the role of the retained porosity on the shock response of additively manufactured high-performance steel: Experiments, constitutive model and finite-element predictions

Experiments have shown that for quasi-static and moderate strain-rates (of the order of 102–103/s) the mechanical response of additively manufactured (AM) and traditionally processed high-strength steels is similar whereas the impact behavior is markedly different. In this paper, we reveal that the main reason for this difference is the retained porosity in the AM material. Fully-implicit finite element calculations are presented in which we simulate both the launching of the impact plate and the impact between the two plates. The constitutive model used is the elastic/plastic model for porous ductile materials with matrix displaying tension-compression asymmetry and Johnson-Cook hardening law that accounts for both strain-rate effects and plastic history. It is shown that even a very small initial porosity changes the wave front, decreases the Hugoniot while increasing the shock rise time, when compared to a void free material. Furthermore, quantitative comparisons between simulation results and plate impact data for both the AM and the wrought AF9628 steel are provided. The good agreement show that the model captures the impact response and illustrates the model capabilities to provide information on field variables that cannot be directly measured.Additive manufacturing (AM) of metals is rapidly advancing as a robust method for production of geometrically complex parts. To enhance understanding of material performance and open up additional application opportunities, dynamic characterization of newly printed alloys is required to validate their effectiveness. In this paper, we present results from plate impact testing of AF9628 steel, a newly developed high-strength low alloy martensitic steel for structural applications which require resistance to high-rate deformation. We put into evidence differences in the shock structure between the AM and the traditionally processed material. To gain understanding, we conduct fully-implicit finite element (FE) calculations in which we model both the launching of the impact plate and the impact between the two plates, respectively. An elastic/plastic damage model that accounts for the effects of the tension-compression asymmetry in plastic deformation and its influence on porosity evolution is used. The FE results reveal that even a very small amount of initial porosity leads to an increase in the shock rise time, explaining the observed trends. Furthermore, quantitative comparisons between simulation results and plate impact data for both the AM and the wrought AF9628 are provided. The good agreement show that the model captures the impact response and illustrates the model capabilities to provide information on field variables that cannot be directly measured.

High-speed grinding: from mechanism to machine tool

AbstractHigh-speed grinding (HSG) is an advanced technology for precision machining of difficult-to-cut materials in aerospace and other fields, which could solve surface burns, defects and improve surface integrity by increasing the linear speed of the grinding wheel. The advantages of HSG have been preliminarily confirmed and the equipment has been built for experimental research, which can achieve a high grinding speed of more than 300 m/s. However, it is not yet widely used in manufacturing due to the insufficient understanding on material removal mechanism and characteristics of HSG machine tool. To fill this gap, this paper provides a comprehensive overview of HSG technologies. A new direction for adding auxiliary process in HSG is proposed. Firstly, the combined influence law of strain hardening, strain rate intensification, and thermal softening effects on material removal mechanism was revealed, and models of material removal strain rate, grinding force and grinding temperature were summarized. Secondly, the constitutive models under high strain rate boundaries were summarized by considering various properties of material and grinding parameters. Thirdly, the change law of material removal mechanism of HSG was revealed when the thermodynamic boundary conditions changed, by introducing lubrication conditions such as minimum quantity lubrication (MQL), nano-lubricant minimum quantity lubrication (NMQL) and cryogenic air (CA). Finally, the mechanical and dynamic characteristics of the key components of HSG machine tool were summarized, including main body, grinding wheel, spindle and dynamic balance system. Based on the content summarized in this paper, the prospect of HSG is put forward. This study establishes a solid foundation for future developments in the field and points to promising directions for further exploration.

Expansion of a hole in a thin plate considering arbitrary smooth pressure-independent yield criterion and work-hardening law

A solution for arbitrary smooth pressure-independent yield criterion and work-hardening law is obtained for the expansion of a hole in an initially uniform infinite plate under plane stress conditions. It is then specialized to widely used yield criteria and work-hardening laws. It is shown that both yield criterion and work-hardening law affect the qualitative behavior of the solution, especially near the hole's surface. In particular, local thickening or thinning may occur there. It is due to the fact that the thickness and yield stress contribute to sustaining the pressure applied to the hole's surface. Therefore, the higher hardening rate requires a smaller thickness. A criterion for the solution's validity applies, and a procedure for using this criterion is developed. Numerical examples illustrate the solution for von Mises and Hosford's yield criteria and Swift's and Voce's hardening laws.

Theory and analytical solutions to wellbore problems with hardening/softening Drucker-Prager models

Recognizing and quantifying the elasto-plastic nature of underground formations is critical for various subsurface operations such as drilling, stimulation, production, injection, and storage. In the case of geological CO2 storage, for instance, it is key to identify storage sites characteristics and pumping parameters that lead to safe and perennial CO2 trapping. In this work, we investigate different rock hardening/softening behaviors with the Drucker-Prager model: cohesion hardening/softening, friction hardening/softening, and their combination, jointed hardening/softening. Our focus is to solve the elasto-plastic deformation analytically in the vicinity of a wellbore. The three hardening/softening formulations predict different mechanical responses and stress-paths for solving the same wellbore problem with excavation. The analytical solutions for 2D axisymmetric problems with different hardening laws are provided in this study and verified with corresponding numerical results. This approach can be used to interpret field observations and calibrate experimental data with more comprehensive models. These new laws are implemented and benchmarked in GEOS, an open-source advanced numerical simulator of subsurface formations. This study enhances our understanding of subsurface rock's elasto-plastic behavior and offer analytical references for interpretating experimental measurements and developing numerical simulations for solving wellbore problems.

An exact rigid/plastic solution for a thick-walled tube subject to internal pressure and axial load considering a general isotropic hardening law and its application

An exact rigid/plastic solution for a thick-walled tube subject to internal pressure and axial load considering a general isotropic hardening law and its application

Modeling Strain Hardening of Metallic Materials with Sigmoidal Function Considering Temperature and Strain Rate Effects.

This study uses a sigmoidal function to describe the plastic strain hardening of metallic materials, considering temperature and strain rate effects. The effectiveness of this approach is evaluated and systematically compared with other hardening laws. Incorporating temperature and strain rate effects into the parameters of this sigmoidal-type hardening law enables a more precise description and prediction of the plastic deformation of materials under different combinations of temperature and strain rate. The temperature effect is coupled using a simplified Arrhenius model, and the strain rate effect is coupled with a modified Johnson-Cook model. The sigmoidal-type hardening law is integrated with an asymmetric yield criterion to address complex behavior, such as anisotropy and strength differential effects. The calibration and validation of the constitutive model involve examining uniaxial tensile/compressive flow curves in various directions and biaxial tensile/compressive flow curves for diverse metallic alloys, proving the proposed model's broad applicability.

Linking Grain Size to Microscopic Hardening Laws in a Phenomenological Crystal Plasticity Model: A Finite Element Simulation Approach for 316L Stainless Steel

Linking Grain Size to Microscopic Hardening Laws in a Phenomenological Crystal Plasticity Model: A Finite Element Simulation Approach for 316L Stainless Steel

A Study on Yield Criteria Influence on Anisotropic Behavior and Fracture Prediction in Deep Drawing SECC Steel Cylindrical Cups.

The deep drawing process, a pivotal technique in sheet metal forming, frequently encounters challenges such as anisotropy-induced defects. This study comprehensively investigates the influence of various yield criteria on the anisotropic behavior and fracture prediction in SECC steel cylindrical cups. It integrates Hill'48R, Hill'48S, and von Mises yield criteria in conjunction with Swift's hardening law to evaluate material behavior under complex stress states. Experimental and numerical simulations assess the anisotropy effects across multiple orientations (0°, 45°, and 90°), revealing intricate relationships between stress criteria and material response. The findings indicate significant discrepancies between isotropic and anisotropic models in predicting fracture heights, emphasizing the importance of selecting appropriate yield criteria. Notably, the von Mises criterion results in lower fracture heights, suggesting higher susceptibility to fractures, while the Hill'48R model aligns closely with experimental data, validated through variations in punch corner radius and blank holder force parameters, with a maximum deviation of 3.23%. Hill'48S displays moderate plastic deformation characteristics.

Investigation of the influence of plane strain constrained anisotropic plastic flow on the localized necking prediction

PurposeThe purpose of this manuscript is to investigate the influence of the satisfying of plane strain conditions on the prediction of the localized necking and to evaluate this effect by the different hardening models.Design/methodology/approachHigh-order anisotropic Drucker yield function, two types of hardening models, namely Hollomon power and Voce saturated, and the modified maximum force criterion (MMFC) are employed to predict the forming limit strains of AA3104-H19 alloy. Two identification methods, namely conventional and plane strain constrained, are applied and forming limit diagrams of the material are predicted by the incorporation of the anisotropic Drucker criterion and the hardening models into the MMFC for both calibration methods.FindingsThe enhancement in the prediction accuracy of the forming limits provided by the implementation of the plane strain constrained method is strongly dependent upon the selected hardening model type in the MMFC. About 18% improvement in the prediction of the biaxial limit strains is provided via Hollomon power law hardening, whereas the opposite result is occurred in case that the Voce saturated hardening law is used, and the predictions match with the experimental data only in the plane strain point and its surroundings.Originality/valueThe plane strain constrained identification method precisely predicts the location of the plane strain point on the yield locus and also any yield stress or anisotropy coefficient in the plane strain state is not required during the calibration, therefore the method can reduce the number of the required experiments for the constitutive characterization, and it will be attractive for both academy and industry. Additionally, the improvement in the prediction of the biaxial forming limits can be provided by applying of this method along with the appropriate hardening law.

An efficient shape-based procedure for strain hardening identification in the post-necking phase

Nowadays, finite element (FE) codes are increasingly employed for simulating large deformation problems. Thus, to reliably represent the strain hardening behavior, a proper calibration of constitutive laws is essential. Focusing on tensile tests, the main issue with ductile metals is necking occurrence, because of the consequent triaxiality and non-uniformity of the strain and stress states. Over the past decades many strain hardening identification approaches have been proposed. Among them, FE-based inverse methods are widely used, but computationally expensive and time consuming. Hence, the authors propose an efficient method which exploits a database for relating the plastic flow rule and the specimen necking profile. The explicit solver of the nonlinear FE code LS-DYNA was used to build the database, whose size could be limited thanks to physical considerations. The developed methodology was applied to experimental quasi-static tensile tests performed on different metals. The predicted hardening laws showed good agreement with those identified with FE-based inverse methods, thus verifying the applicability of the proposed strategy. This study paves the way for machine learning tools having as main input the necking shape: indeed, the present work suggests their feasibility and provides insights into how to establish datasets for a proper and efficient training.

A macro-micro approach for identifying crystal plasticity parameters for necking and failure in nickel-based alloy haynes 282

This work develops a two-scales macro-micro approach to address the challenge in calibrating crystal plasticity microstructural models when samples undergo necking prior to fracture. The crystal plasticity models are crucial for predicting the materials’ plastic deformation and failure at the microstructure level, identifying the materials’ intrinsic properties as well as investigating the microstructure-properties relationships. However, after necking occurs, the experimentally measured stress-strain curves fail to reflect the materials ‘true’ stress-strain behavior and cannot be directly fitted into crystal plasticity models. The proposed macro-micro approach employs a top-down strategy to address this challenge, which has been studied with experimental tests on precipitation-strengthened Ni-based superalloy Haynes® 282®. In this approach, a macro rate-dependent anisotropic plasticity model with Voce-type hardening and Rice-Tracey damage law is first utilized to model the deformation and failure of the tensile bar, and calibrated by matching the stress-strain curves, necking strain, and reduction of area. Especially, to match the testing results under different applied strain rates, the rate-sensitivity parameter m and saturation stress in the elasticity model are modified to incorporate dependence on the local strain rate. Then, the ‘true’ stress-strain behaviors are extracted from the necking zone of the macro-model, which are used to calibrate a micro-model with explicit microstructures and governed by an extended crystal plasticity law. The consistency between the micro-model and macro-model are enforced during calibration. The calibration outcomes from the crystal plasticity model elucidate the materials intrinsic properties for slip, hardening, and failure, which is vital for further investigations into the microstructure-properties relationship and for accurate prediction of the material behavior under various test and service conditions.

Effect of the loading-rate and stress state on the constitutive modelling and fracture of 2205 Duplex stainless steel

Shear cutting is a high-speed forming process where material separation is involved. The nature of the process leads to high strain rates and temperatures on the sheared zone of the material subjected to the operation. In this work, the mechanical behavior in terms of flow stress, plastic deformation and fracture of a 2205 Duplex stainless steel sheet is determined. Uniaxial tension, uniaxial compression, stack compression, plane strain tension and simple shear tests at different angles with respect to the rolling direction of the metal sheet are performed to determine the anisotropic behavior of the material. Strain rate and temperature dependence of the flow stress and the plastic behavior of the material is determined through notched tensile tests performed under various temperatures (20°C, 100°C, 300°C and 500°C) and strain rates (0.001 s-1, 10 s-1 and >100 s-1). Finally, fracture behavior under various stress states is determined through notched tensile, central hole, in-plane shear and plane strain tests. The temperature and strain rate dependence of the fracture behavior is determined through notched tensile, in-plane shear and plane strain tests performed under various temperatures (20°C, 100°C, 300°C and 500°C) and strain rates (0.001 s-1, 10 s-1 and >100 s-1). The anisotropic behavior and work hardening of the material are modelled by the Hill48 yield function and Swift-Hockett-Sherby hardening law, respectively. Among the two ductile fracture models tested, Hosford-Coulomb model showed the best agreement and is therefore used to account for the temperature and strain rate effects on the fracture behavior. By combining these three models, an accurate reproduction of the mechanical behavior of the 2205 Duplex stainless steel sheet is achieved.

Deep drawing simulation of dual phase steel using hardening curves and anisotropic parameters from uniaxial and biaxial tensile tests

Among the various factors, the accuracy of the predictions from the numerical simulation of sheet metal forming processes depends on the material model used to define the mechanical behavior of the blank material. The coefficients of the hardening model to define the flow curve and the plastic strain ratios are commonly determined using the uniaxial tensile tests. The advanced anisotropic yield criteria incorporate material flow behaviour and plastic strain ratio in equi-biaxial tension. In this work, deep drawing of a flat bottom cylindrical cup has been simulated using dual-phase steel (DP600) sheets. The biaxial material properties obtained by conducting hydraulic bulge test and cruciform specimen test are used in the anisotropic yield criteria in the simulations. The hardening curves are extrapolated using different hardening laws in which the coefficients are determined from the stress-strain curves obtained from both uniaxial tensile and hydraulic bulge tests. The predicted peak drawing load and thickness variation in the drawn cups are compared with the experimental results of deep drawing.

Post-fire mechanical properties and constitutive model of Q690 high-strength structural steel

Fire hazard is one of the main threats to the integrity of steel structural buildings. Developing an accurate post-fire constitutive model for structural steel is crucial for enhancing the failure assessment of steel structures exposed to fire. In this study, the post-fire mechanical behavior of Q690 high-strength structural steel is investigated. Eighteen round bar specimens made of Q690 steel were heated with temperatures ranging from 20 °C to 900 °C. Tensile tests were conducted on these specimens to obtain the post-fire stress-strain curves and associated mechanical parameters of the material. To accurately characterize the post-fire behavior of Q690 steel, a temperature-dependent elastoplastic constitutive model combined with its numerical implementation algorithm is proposed. This model consists of four components: a temperature-dependent elasticity criterion, the von Mises yield criterion, an associated flow rule, and a temperature-dependent isotropic hardening law. The proposed constitutive model has a notable feature, i.e. the material parameters in the model can be defined as a function of temperature according to the test results. As a result, when utilizing this model for post-fire assessments of steel members, only three routine parameters, i.e. elastic modulus at room temperature, Poisson's ratio, and the temperature experienced by the material, are required in the numerical simulation to generate the material’s stress-strain relationships. To verify the proposed constitutive model, the new model was introduced into the numerical simulations of the tested round bar specimens after exposure to various temperature conditions. Both the load-displacement curves and local deformation of each round bar specimen obtained from the numerical simulations are compared with the test results to validate the accuracy of the new model. The constitutive model presented in this study provides a useful tool for assessing the post-fire behaviors of steel components.

Size effects in spherical indentation of single crystal copper

A study of the size effects in the spherical indentation test of a copper single crystal is carried out. The main novelty of the approach is the analysis of a wide spectrum of parameters measured in the test that are predicted by the proposed model, and the prediction is verified experimentally for six different tip radii. Load-penetration depth curves, nominal hardness, pile-up and sink-in profiles, and the rotation and rotation gradient of the crystallographic lattice in the cross-section beneath the indenter have been measured and also calculated using 3D finite element simulations on the micro- and nanometer scale. Two gradient-effects are examined numerically within the Cosserat elastoplasticity framework with the gradient-enhanced hardening law. It is shown that a good prediction of the experimentally observed size effect on nominal hardness is achieved using the conventional power-hardening law, calibrated from the standard uniaxial compression test, enhanced with a term dependent on the lattice spin gradient term with no adjustable parameter. Furthermore, it has been found that the observed distribution of lattice rotation and decrease in the rotation magnitude with decreasing indenter radius can be qualitatively modelled by adjusting the coefficient of accumulated lattice curvature energy within the same framework.

Topology Optimization and Efficiency Evaluation of Short-Fiber-Reinforced Composite Structures Considering Anisotropy

The current study aims to develop a methodology for obtaining topology-optimal structures made of short fiber-reinforced polymers. Each iteration of topology optimization involves two consecutive steps: the first is a simulation of the injection molding process for obtaining the fiber orientation tensor, and the second is a structural analysis with anisotropic material properties. Accounting for the molding process during the internal iterations of topology optimization makes it possible to enhance the weight efficiency of structures—a crucial aspect, especially in aerospace. Anisotropy is considered through the fiber orientation tensor, which is modeled by solving the plastic molding equations for non-Newtonian fluids and then introduced as a variable in the stiffness matrix during the structural analysis. Structural analysis using a linear anisotropic material model was employed within the topology optimization. For verification, a non-linear elasto-plastic material model was used based on an exponential-and-linear hardening law. The evaluation of weight efficiency in structures composed of short-reinforced composite materials using a dimensionless criterion is addressed. Experimental verification was performed to confirm the validity of the developed methodology. The evidence illustrates that considering anisotropy leads to stiffer structures, and structural elements should be oriented in the direction of maximal stiffness. The load-carrying factor is expressed in terms of failure criteria. The presented multidisciplinary methodology can be used to improve the quality of the design of structures made of short fiber-reinforced composites (SFRC), where high stiffness, high strength, and minimum mass are the primary required structural characteristics.

A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils

A multiscale method is presented to develop a constitutive model for anisotropic soils in a three-dimensional (3D) stress state. A fabric tensor and its evolution, which quantify the particle arrangement at the microscale, are adopted to describe the effects of the inherent and induced anisotropy on the mechanical behaviors at the macroscale. Using two steps of stress mapping, the deformation and failure of anisotropic soil under the 3D stress state are equivalent to those of isotropic soil under the triaxial compression stress state. A series of discrete element method (DEM) simulations are conducted to preliminarily verify this equivalence. Based on the above method, the obtained anisotropic yield surface is continuous and smooth. Then, a fabric evolution law is established according to the DEM simulation results. Compared with the rotational hardening law, the fabric evolution law can also make the yield surface rotate during the loading process, and it can grasp the microscopic mechanism of soil deformation. As an example, an anisotropic modified Cam-clay model is developed, and its performance validates the ability of the proposed method to account for the effect of soil anisotropy.

Analysis of TRIP Steel HCT690 Deformation Behaviour for Prediction of the Deformation Process and Spring-Back of the Material via Numerical Simulation.

This paper deals with the analysis of TRIP steel HCT690 deformation behaviour. The mechanical properties and deformation characteristics of the tested material are determined using selected material tests and tests that consider the required stress states used to define the yield criterion boundary condition and subsequent deformation behaviour in the region of severe plastic deformation. The measured data are subsequently implemented in the numerical simulation of sheet metal forming, where they are used as input data for the computational process in the form of a selected material model defining the yield criterion boundary and, furthermore, the material hardening law during deformation of the material. The chosen numerical simulation process corresponds to the sheet metal forming process, including the subsequent spring-back of the material, when the force does not affect the material. Furthermore, the influence of the chosen computational model and selected process parameters on the deformation and spring-back process of the material is evaluated. In addition to that, at the end of the paper, the results from the numerical simulation are compared with experimentally produced sheet stamping.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction. This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures. The issue stems from the pressure independent hardening law in the classical deviatoric hardening model. To overcome this problem, we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations. Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands. Furthermore, to examine the importance of the improved deviatoric hardening model, it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures. It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

STRENGTH AND DUCTILITY CHARACTERISTICS OF METAL ALLOYS AND STAINLESS STEELS CREATED BY WIRE-ARC SURFACING IN A WIDE RANGE OF STRAIN RATES

To select rational parameters of the process of hybrid additive manufacturing of structures made of structural metal alloys and stainless steels, mechanical characteristics capable of serving as indicators of material quality were determined. The most advanced technologies of additive manufacturing by wire-arc surfacing (plasma, plasma arc with a melting electrode, including cold metal transfer) with layer-by-layer forging with a pneumatic impact tool and subsequent heat treatment were used. Aluminum-magnesium alloy AlMg5, titanium alloy Ti-6Al-4V, austenitic stainless steels 12Cr18Ni10Ti (AISI 321) and AISI 308LSi have been studied. Samples were cut from the blanks created by additive manufacturing – blades for standard tests for static uniaxial tension and cylinders for high-speed compression tests by the Kolsky method on a Hopkinson split bar. According to the registered and processed stress–strain curves for all materials, standard strength and ductility characteristics and the Johnson – Cook law of deformation and speed hardening were determined. For a correct assessment of the mechanical properties of additively produced materials, these tests were also carried out for each of them in the form of annealed rolled products. It is established that to compare the efficiency of various technological parameters of additive manufacturing, it is advisable to use static tensile strength and uniform elongation to rupture, having the smallest statistical variation. It was also found acceptable to approximate the Johnson – Cook law of the deformation curves of each of the studied materials according to averaged data, including various technological modes. Certain mechanical characteristics seem to be necessary for the search for effective modes of hybrid additive manufacturing and numerical calculation of various elastic-plastic problems in a dynamic formulation for the studied materials for design and technological needs.