Hybrid Experimental-numerical Method Research Articles

Dynamic tensile behavior and constitutive model of a novel high-strength and high-toughness plate steel

The dynamic tensile behavior of a novel-developed plate steel with high strength and toughness is investigated. Uniaxial tensile tests are conducted at various strain rates varying from 0.1 s−1 to 1000 s−1, and then scanning electron microscope and electron backscattered diffraction analyses are performed on tensile specimens at failure. A large and homogeneous deformation is demonstrated during the tension and small necking is observed at failure; all test results reveal the strain rate dependency of this novel plate steel: with an increase in strain rate, the yield strength, ultimate tensile strength, and total elongation increase, whereas the uniform elongation decreases. Microstructure analyses find dimple fracture surface and considerable deformation twins and dislocations, confirming the high strength and high ductility of the novel plate steel. The density of twins and dislocations demonstrates a positive correlation with the increasing strain rate, aligning with the variations observed in the mechanical properties. Engineering stress–strain curves exhibit a necking lag effect at high strain rates, and this effect is considered when solving the true stress–strain relationships by a developed hybrid experimental–numerical method. A modified Johnson-Cook model considering the power law strain rate effect and thermal softening effect caused by adiabatic temperature rise is finally proposed and verified. This work explores the dynamic mechanical behavior of the novel plate steel at different strain rates, promoting its application in aseismic design and impact resistance engineering.

Ductile Fracture Prediction in Hole Hemming of Aluminum and Magnesium Sheets

The present work proposes a suitable approach for predicting ductile fracture in a new joining process by plastic deformation called hole hemming. This process creates a combined form- and force-fit joint and enables the joining of lightweight materials with varying formability without requiring heating or auxiliary elements. In this process, the joinability of materials is limited by the occurrence of fracture in the outer sheet, highlighting the crucial need to accurately predict its damage during the process design phase. In this study, five different fracture criteria, including the McClintock, Rice–Tracey, Normalized Cockroft–Latham, and Brozzo and Modified Mohr–Coulomb (MMC) criteria, are examined during the joining of a challenging combination of lightweight materials (aluminum AA6082-T4 and magnesium AZ31). These criteria are calibrated by a hybrid experimental–numerical method using three tests with distinct stress states. These criteria are then implemented into the finite element model of the hole hemming process, utilizing an appropriate user subroutine. The results show that the flange edge of the outer sheet is the most prone region to fracture during the joining process, and a criterion must be able to model the fracture behavior of the material from uniaxial tension to shear to accurately predict fracture in this area. Among the examined criteria, only the MMC criterion was capable of such modeling and accurately predicted the critical displacement of the punch in the hemming stage with a negligible error (about 1%). On the other hand, the prediction accuracy of the other criteria varied significantly depending on the calibration test, resulting in errors ranging from 8.6% to 75.5%. The error of 8.6% was achieved with the Normalized Cockroft–Latham criterion calibrated by a uniaxial tension test. Thus, based on the results, the MMC criterion is recommended for ductile fracture prediction in the hole hemming process, offering valuable insights to assist in process design.

Identification of elastic and plastic properties of aluminum-polymer laminated pouch film for lithium-ion batteries: A hybrid experimental-numerical scheme

Lithium-ion batteries (LIBs) are crucial components for electric vehicles (EVs), and their mechanical and structural stabilities are of paramount importance. In this study, the mechanical properties of an aluminum-laminated pouch sheet, as a key component of pouch-type LIBs, are examined. Aluminum-laminated pouch sheets have rarely been systematically investigated in the past. Owing to the complex composite structure of pouch sheets having metallic and polymeric materials, fully understanding and describing their mechanical responses is scientifically challenging without data or knowledge of the individual materials. Therefore, the prime novelty of the present study is to identify the elastic and plastic properties of the individual material components of a pouch sheet. In particular, we propose an efficient and user-friendly methods that physically separate all material layers by applying a novel hybrid experimental-numerical method based on the full-field strain measurement and finite element simulation. The identified mechanical properties and their constitutive models are validated using a tensile test and the square cup formability test of the pouch sheet. The determined data from the proposed methods can provide valuable insights into the mechanical behavior of LIBs, which can assist the new design of pouch sheets used for more mechanically stable Li-ion batteries with enhanced energy storage performance.

A Hybrid Experimental-Numerical Method to Support the Design of Multistage Pumps

The paper uses a hydraulic performance analysis method to support the design of stock production multistage pumps. The method relies on a hybrid numerical–experimental approach conceived as a trade-off between accuracy and cost. It is based on CFD analyses incorporating experimental data of leakage flows across the sealing elements to obtain accurate predictions without the need of inclusion in the CFD model of small-scale features, which strongly increase the model complexity and computational effort. The aim of the paper is to present and validate this method. To this end, a 6-stage vertical pump manufactured by the stainless-steel metal-sheets-forming technique was considered as the benchmark. A series of experimental tests were performed to hydraulically characterize the impeller and return-channels-sealing elements by means of an “ad hoc” designed test rig. The characteristic curves of the sealing elements were embedded on the CFD model implemented in accordance with the strategy proposed in a previous authors’ work to obtain satisfactory predictions of multistage pumps’ hydraulic performance with minimum computational effort with the analytical correction of single-stage single-channel computations to account for the interaction between adjacent stages. To further explore the capabilities of the hybrid model, axial thrust measurements were performed by means of another “ad hoc” designed experimental apparatus. The application of the method to the benchmark pump shows that the hybrid model predicts the static head and efficiency with an error value lower than 1% at its best efficiency operation, and estimates the axial thrust with a 5% average error in the operating range from approximately 70% to 120% of the best efficiency duty.

A ductile fracture model incorporating stress state effect

To understand comprehensively the relationship between material ductility and stress state, the new shear, shear-compression, and shear-tension specimens were specially designed, and seven types of specimens were used in total to achieve precise control of stress states over wide ranges of stress triaxialities and Lode angle parameters. A hybrid experimental-numerical method was employed to determine the equivalent plastic strain, stress triaxiality, and Lode angle parameter, and hence to construct the 3D fracture locus of the Ti-6Al-4V alloy. Different micromechanisms were found to dominate the failure process under various stress states. Based on the experimental results, a new ductile fracture model coupling both stress triaxiality and Lode angle parameter was proposed and implemented into the commercial finite element program ABAQUS/Explicit via the user material subroutine VUMAT. Comparative studies with some other fracture criteria indicate that the proposed fracture model can capture the non-monotonic feature of fracture strain, and predict the fracture strain with better accuracy in a wide range of stress states. A verification test was performed to check the predictive capability of the present model. The results show the excellent agreement between experiment and simulation with respect to the fracture displacement and fracture morphology. This study paves the way for characterizing and predicting the ductile behavior of metallic materials under complex stress states, and provides a fundamental databank for the analysis and design of Ti-6Al-4V alloy structures.

Multi-Criteria Evaluation of the Failure of CFRP Laminates for Frames in the Automotive Industry.

Methods to predict the fracture of thin carbon fibre-reinforced polymers (CFRPs) under load are of great interest in the automotive industry. The manufacturing of composites involves a high risk of defect occurrence, and the identification of those that lead to failure increases the functional reliability and decreases costs. The performance of CFRPs can be significantly reduced in assembled structures containing stress concentrators. This paper presents a hybrid experimental-numerical method based on the Tsai-Hill criterion for behavior of thin CFRPs at complex loadings that can emphasize the threshold of stress by tracing the σ-τ envelope. Modified butterfly samples were made for shearing, traction, or shearing-with-traction tests in the weakened section by changing the angle of force application α. ANSYS simulations were used to determine the zones of maximum stress concentration. For thin CFRP samples tested with stacking sequences [0]8 and [(45/0)2]s, the main mechanical characteristics have been determined using a Dynamic Mechanical Analyzer (DMA) and ultrasound tests. A modified Arcan device (AD) was used to generate data in a biaxial stress state, leading to the characterization of the material as a whole. The generated failure envelope allows for the prediction of failure for other combinations of normal and shear stress, depending on the thickness of the laminations, the stacking order, the pretension of the fasteners, and the method used to produce the laminations. The experimental data using AD and the application of the Tsai-Hill criterion serve to the increase the safety of CFRP components.

Evaluation of mode II fracture toughness under high loading rate conditions for composite bonded joints

Composite bonded joints are widely used in the aircraft components, which are frequently subjected to impact loading. The present paper intends to evaluate the mode II fracture behavior of composite bonded joints under high loading rate conditions. Dynamic loading was applied on the end-notched flexure (ENF) specimen at 10 m/s and 15 m/s via an electromagnetic split Hopkinson pressure bar system. Then the dynamic fracture toughness was evaluated using an experimental-numerical hybrid method according to the virtual crack-closure technique and compared to the fracture toughness under quasi-static loading rate (2 × 10−5 m/s and 2 × 10−4 m/s). Results indicate that the mode II fracture toughness of adhesively bonded composite joints shows a positive rate-dependent trend. The mode II fracture toughness can increase about 31.5% when the loading rate increases to 15 m/s. At last, fracture surface inspections using scanning electron microscopy (SEM) were conducted to reveal the physical mark of such an effect.

Modeling the crashworthiness analysis of functional graded strength thin-walled structure with phenomenological GISSMO model

In this paper, the phenomenological generalized incremental stress–strain model (GISSMO) is investigated to predict the damage-mechanical behavior of the quenched boron steel. Four fracture strain vs. stress triaxiality hyperbolic curves of quenched boron steels with different hardness are established employing a hybrid experimental–numerical method, and the corresponding damage parameters m and n are further identified by the FE inverse method using a multi-objective particle swarm optimization algorithm (MOPSO). Subsequently, a tailored partial quenching process is employed to fabricate the two-segment functional graded strength (FGS) and the uniform strength (US) hat-shaped structures, and their experimental and simulated crashworthiness is further investigated to validate the effectiveness of the established GISSMO model. Compared to the simulation with the failure plastic strain and the simulation without damage model, simulated results with GISSMO model of US structure match the best with the experimental result in terms of both deformation mode and force vs. deformation curve. And the error of SEA is no more than 6%. Results of the FGS structure also demonstrated a good consistency between simulation with GISSMO model and the experiment. In terms of SEA and CFE, the predicted accuracy was improved from 13.437%, 23.404% to 9.140%, 6.687%, respectively by adding the GISSMO model in simulation. Thus, it indicates that modeling with the GISSMO model is highly adequate to predict the crashworthiness of the quenched boron steel for both US and tailored FGS structures.

Characterizing springback stress behavior in VPB by experimental-numerical hybrid method

Springback is a stress-driven phenomenon during unloading, so the stress behavior during unloading is of great significance for exploring and understanding springback. However, the accuracy of stress field after loading procedure in FEM, as the basis of springback simulation, is greatly affected by the assumptions of material model and boundary condition. Moreover, the selection of constraints in springback simulation is crucial and highly subjective, thus affecting the authenticity of results. In this paper, the characteristic of springback stress is studied in viscous pressure bulging (VPB) using an experimental-numerical hybrid method, combining the DIC method and numerical calculation. The springback results under different viscous mediums are obtained and their laws are discussed. The measured springback data containing the information of material properties and boundary conditions are used to calculate springback stress by the presented numerical calculation program. The springback stresses of sections along rolling direction and transverse direction are obtained. The variation law of the magnitude and direction of springback stress vector with springback is revealed. Then the mechanism of springback stress variation and the springback reduction are analyzed. Results show that the springback stress conforming to objective and practical conditions can be obtained, and it changes regularly with springback. The viscous medium affects the shape and stress of sheet, causing the change of springback stress. Furthermore, the change of springback stress reduces the reverse bending moment to restrain the resulting springback.

Effects of strain path and girth weld heterogeneity on strain limits of X70 pipeline

Geological disasters frequently cause pipeline failure. Therefore, the strain limits of pipelines under various strain paths should be carefully considered to provide the critical strain, particularly for girth welds. The iterative method was used to determine local accurate constitutive relations for the three typical zones of X70 girth weld: base material (BM), heat affected zone (HAZ), and welding metal (WM). By combing accurate constitutive equations of local deformation with a modified elliptical fracture criterion. The prediction strain limits were then verified using a hybrid experimental-numerical method with four geometries (uniaxial tension, tension with notch, flat-groove tension, and pure shear specimens) and three zones (BM, HAZ, and WM). The microstructure and fractography of BM, HAZ, and WM zones were analyzed to investigate the difference in strain limits under different strain paths. The results demonstrate that in tension stress states, the strain limits of WM for under-matched girth welds are the weakest, while the tension-compression asymmetry for WM is the greatest. As a result, when a pipeline is under tension, the girth weld is prioritized for protection. On the other side, the pipeline itself focuses on protection in compression to avoid buckling. Furthermore, the ferrite content is mostly responsible for the contribution of strain limits for these zones. The lower strain limit of WM in the tensile state is attributable to the inclusions in the welding process.

Damage Evolution of Hot Stamped Boron Steels Subjected to Various Stress States: Macro/Micro-Scale Experiments and Simulations.

Hot stamping components with tailored mechanical properties have excellent safety-related performance in the field of lightweight manufacturing. In this paper, the constitutive relation and damage evolution of bainite, martensite, and mixed bainite/martensite (B/M) phase were studied. Two-dimensional representative volume element (RVE) models were constructed according to microstructure characteristics. The constitutive relations of individual phases were defined based on the dislocation strengthening theory. Results showed that the damage initiation and evolution of martensite and bainite phases can well described by the Lou-Huh damage criterion (DF2015) determined by the hybrid experimental–numerical method. The calibrated damage parameters of each phase were applied to the numerical simulation, followed by the 2D RVE simulations of B/M phase under different stress states. To study the influence of martensite volume fraction (Vm) and distribution of damage evolution, the void nucleation and growth were evaluated by RVEs and verified by scanning electron microscope (SEM). Three types of void nucleation modes under different stress states were experimentally and numerically studied. The results showed that with the increase of Vm and varying martensite distribution, the nucleation location of voids move from bainite to martensite.

A unified model of ductile fracture considering strain rate and temperature under the complex stress states

In the thermoforming process of complex components, such as the multi-directional loading forming of multi-cavity parts, complex stress states always exist and change. Meanwhile ductile fracture is prone to occurring, which is sensitive to stress state, as well as deformation temperature and strain rate. This makes fracture behavior very complex and prediction for it difficult. In this paper, a new type of fracture test device was developed, also a trapezoidal groove shape (TGS) specimen was ingeniously designed to change the stress state from tension-shear to pure shear and compression-shear only by increasing the groove bridge angle β. The fracture behaviors of AA7075-H112 under strain states 0.04s−1∼1s−1 and temperatures 20 °C∼450 °C were studied, and the fracture mechanism was identified as a mixture of surface shear and core tensile fracture, but an increasing β promoted the formation and proportion of shear plane and finally led to shear fracture. Based on this, a shear-dominated DF2014 model was determined as the basic framework, then the temperature and strain rate terms of Johnson-Cook fracture model were referenced and modified to be introduced, and finally a unified thermoforming fracture model under various complex stress states was established. The full set of model parameters was determined by a hybrid experimental-numerical method and the predictions of model were verified to match the experimental ones. Then the distribution of critical equivalent strains to fracture was presented in space of stress triaxiality and Lode parameter, which showed a good predictive capability over a wide stress state range with low stress triaxialities.

Estimating residual stresses of silicon wafer from measured full-field deflection distribution

This paper proposes an experimental-numerical hybrid method for estimating the residual stresses in a silicon wafer from the full-field deflection measurement. In the proposed method, the measured deflection distribution is approximated using regularized least-squares based on the superposition principle. Simultaneously, the residual stresses induced with the deflection are estimated. By applying the proposed method to a deflection distribution by finite element simulation, the basic principle of the proposed method is verified. Then, the proposed method is applied to the steel plate specimens mimicking a silicon wafer. The residual stresses obtained using the proposed method are compared with the results obtained using the X-ray diffraction method, and the appropriate regularization parameter is determined. Finally, the proposed method is successfully applied to the residual stress estimation of an actual silicon wafer. Because the deflection of a silicon is often measured during the inspection process, the proposed method of using the deflection to estimate the residual stresses is useful. Therefore, the proposed method is expected to be applied to the inspection process of silicon wafers.

Nanomechanical Characterization of the Deformation Response of Orthotropic Ti–6Al–4V

The nanoindentation‐induced mechanical deformation response is applied to identify the orthotropic elastic moduli using the Delafargue and Ulm method as well as to validate the asymmetric orthotropic CPB06 nonlinear plasticity model required in simulations of nonuniform macroscopic mechanical response of the Ti–6Al–4V alloy. Scanning electron microscope (SEM) technique allows to select the maximum penetration depth for the indentation in the deformed alpha phase and alpha–beta interphase,αandα/β, respectively. The apparent macromechanical response can be successfully derived from several residual imprints conducted at micro‐ and/or submicrometric length scale and distributed throughout samples of the investigated bulk alloy, as demonstrated by correlation with finite element simulations based on the orthotropic elastoplastic model. The accurate numerical response obtained validates the material model and the Delafargue and Ulm approach, opening a window for next generation identification methods of macromechanical plasticity models with hybrid experimental–numerical method based on instrumented indentation and the use of SEM technique.

Visual indentation apparatus and finite element modelling as a method to characterize 3D mechanical properties of facial skin in vivo

Knowledge of the mechanical properties of human skin has essential applications in cosmetic, dermatology and surgical fields. In this study, a hybrid experimental–numerical method was developed to characterize the human skin mechanical properties in vivo. An indentation experiment was physically conducted and simulated by finite element (FE) analysis. In the physical experiment, an indenter made of transparent glass was adopted so that the elliptical eccentricity in the contact area between skin and indenter could be monitored in real-time. In FE simulation, the dermis and subcutaneous tissue were modeled as anisotropic hyperelastic material and isotropic elastic material, respectively. By fitting the FE results to the experimental data, the three-dimensional (3D) mechanical properties of skin, including the dermis and subcutaneous tissue were determined. Furthermore, to demonstrate the ineffectiveness of the hybrid experimental–numerical method, a sensitivity analysis was conducted. In this sensitivity analysis, it is shown that the different mechanical parameters have a different contribution to the final FE result. Finally, the effect of subcutaneous tissue for in vivo skin indentation measurement was also evaluated.

Shear Stress Hardening Curves of AISI 4130 Steel at Ultra-high Strain Rates with Taylor Impact Tests

This paper is concerned with shear properties of AISI 4130 steel at various strain rates from the quasi-static state to ultra-high strain rates using a Taylor impact testing machine. Shear properties of metallic materials are known to be sensitive to the strain rate especially at high strain rates. In order to investigate hardening behavior under shear loading, in-plane shear tests are carried out at a wide range of strain rates from 10–3 s–1 to 103 s–1 with an INSTRON 5583 and a High Speed Material Testing Machine with a novel procedure to obtain hardening curves from shear tests. To induce shear deformation at ultra-high strain rates, a novel shear specimen applicable to Taylor impact tests is designed and then shear tests are conducted with a Taylor impact testing machine. Hardening curves are extrapolated by a dynamic hardening model and then calibrated by an experimental–numerical hybrid method with an inverse optimization scheme so that finite element analysis results match to shear tests results at ultra-high strain rates with the Taylor impact test. Shear fracture strains at ultra-high strain rates are also calibrated in the same manner. Calibrated flow stresses are higher than the extrapolated ones before calibration and calibrated shear fracture strains decrease more rapidly than the extrapolated ones before calibration at the ultra-high strain rate region.

Prediction of ductile fracture on 6016-T4 aluminum alloy sheet metal forming considering anisotropic plasticity

This study is aimed to predict ductile fracture of sheet metal forming for 6016-T4 aluminum alloy (AA6016-T4). Six shapes of tension tests in three directions with respect to the rolling direction have been carried out up to fracture to measure ductile fracture for the sheet. Since the fracture-related parameters determined by finite element simulation are sensitive to plasticity model, the Yld2000-2d and anisotropic Drucker yield functions with a combined Swift-Voce hardening model were firstly identified for AA6016-T4 and then used to compare the prediction accuracy. These constitutive models are implemented into ABAQUS for plane stress condition and S4R shell elements are set for the finite element model. Comparison of the experimental and simulation results indicates that the anisotropic Drucker yield function is more suitable for AA6016-T4 by considering both the computational accuracy and efficiency. Based on these results, fracture loci for AA6016-T4 were represented by four common ductile fracture criteria (Cockcroft–Latham, Rice–Tracey, Clift and DF2012). Three kinds of specimen were employed to calibrate the fracture models by using a hybrid experimental–numerical method. The results show that the DF2012 criterion is more flexible and accurate for AA6016-T4 with the comparison of force–displacement curves. For further validation, these four ductile fracture criteria are also applied to predict the fracture of an automobile inner panel in drawing forming, and the results show that the DF2012 criterion provides sufficient prediction precision for AA6016-T4.

Enhanced CDM model accounting of stress triaxiality and Lode angle for ductile damage prediction in metal forming

This paper deals with the prediction of ductile damage based on CDM approach fully coupled with advanced elastoplastic constitutive equations. This fully coupled damage model is developed based on the total energy equivalence assumption under the thermodynamics of irreversible processes framework with state variables. In this model, the damage evolution is enhanced by accounting for both stress triaxiality and Lode angle. The proposed constitutive equations are implemented into Finite Element (FE) code ABAQUS/Explicit through a user material subroutine (VUMAT). The material parameters are determined by the hybrid experimental-numerical method using various tensile and shear tests. Validation of the proposed model has been done using different tests of two aluminum alloys (Al6061-T6 and Al6014-T4). Through comparisons of numerical simulations with experimental results for different loading paths, the predictive capabilities of the proposed model have been shown. The model is found to be able to capture the initiation as well as propagation of macro-crack in sheet and bulk metals during their forming processes.

Experimental and numerical investigation of deformation characteristics during tube spinning

The primary objective of this study is to predict the geometric shape and thickness change during multi-pass tube spinning to a hemispherical shape. A computationally efficient, axisymmetric finite element model of the tube-spinning experiments is described. Uniaxial tensile tests are conducted for the development of the material model. The post-necking hardening curve is identified using a hybrid experimental-numerical method and represented by a combined Swift-Voce model. For validation of the finite element model, spinning experiments are performed at room temperature on thin-walled cylinders of 6061-O aluminum alloy. The experiments are interrupted after spinning passes 2, 4, 6, and 8 and the shape and thickness are measured. Also, local strain measurements on the final spun tube (pass 8) are accomplished by a scribed grid. By comparing the predictions to the experiments, good agreement is obtained on the shape, thickness, and strain evolution in multi-pass spinning. The deformation mechanism of this process is described by analyzing the history of plastic strain on an element of the numerical model.

Fracture Prediction for an Advanced High-Strength Steel Sheet Using the Fully Coupled Elastoplastic Damage Model with Stress-State Dependence

In this study, the numerical simulations of sheet metal forming processes are performed based on a fully coupled elastoplastic damage model. The effects of stress triaxiality and Lode angle are introduced into the damage evolution law to capture the loading-path-dependent failure. The proposed constitutive model is implemented into the finite element (FE) code ABAQUS/Explicit via the user-defined subroutine (VUMAT). Next, the identification procedure for DP780 based on the hybrid experimental–numerical method is presented in detail. The numerical results of simple tests are compared with the experiments, and obvious improvement is observed for the proposed model under various loading paths. Finally, the model is applied to predict the edge fracture during sheet blanking process. The predicted global load–displacement responses and crack paths have a good agreement with the experimental results, indicating that the model holds great potentials in simulation of metal forming processes.