Experimental Load Displacement Research Articles

Identification of material parameters of the Gurson–Tvergaard–Needleman damage law by combined experimental, numerical sheet metal blanking techniques and artificial neural networks approach

This paper presents a method for the identification of coupled damage model parameters in sheet metal blanking and a study of their sensitivity to the blanking clearance. The existing finite element models easily describe the elastoplastic behaviour occurring during the sheet metal blanking. However, the description of the damage evolution is much more delicate to appreciate. The proposed method combines finite element method (FEM) with artificial neural networks (ANN) analysis in order to identify the values of the Gurson-Tvergaard-Needleman (GTN) parameters. The blanking tests are carried out to obtain the experimental material response under loading (blanking force—blanking penetration curves). A finite element model is used to compute the load displacement curve depending on a systematic variation of GTN parameters. Via a full factorial design, a numerical database is built up and is used for the ANN training. The identification of the damage properties (for a fixed clearance) is done by minimizing the error between an experimental load displacement curve and a predicted one by the ANN function. The identified damage law parameters are validated on the other experimental configurations of blanking tests (fixed clearance, different punch velocities). Varying the blanking clearance allows us to study its impact on the damage law parameters.

Micro-cantilever testing of ⟨a⟩ prismatic slip in commercially pure Ti

Four sizes (1, 2, 5 and 10 µm wide) of single-crystal α-Ti micro-cantilevers were manufactured from polycrystalline commercially pure Ti samples using a focussed ion beam. A nanoindenter was used to conduct micro-bending tests. The crystal orientation and alignment of the micro-cantilever beams were selected so as to activate only ⟨a⟩ slip on prism planes. A crystal plasticity finite element model was used to simulate the deflection behaviour of the cantilevers. The critical resolved shear stresses (CRSS) were determined via a reverse process of fitting the simulation results to the experimental load–displacement curves. The CRSS increased from 144 MPa for the 10 µm wide cantilevers to 566 MPa for the 1 µm wide cantilevers.

EXtended Finite Element Method for fracture characterization of adhesive joints in pure mode I

Adhesive-bonding for the unions in structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of reliable damage models to predict their fracture behaviour. Cohesive Zone Models (CZM’s) have been extensively used in the past, taking advantage of traction-separation laws between stresses and relative displacements to simulate crack growth along predefined paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on damage laws based on the bulk strength of materials for damage initiation and strain for the assessment of failure, rather than the tipping tractions and tensile/shear relative displacements used for the CZM’s. Compared to the FEM, XFEM excels in allowing discontinuities to grow within bulk solids along an arbitrary path. This work aims to assess the viability of the XFEM to predict the fracture behaviour of a thin layer of adhesive between stiff and compliant adherends. To build the XFEM damage laws, the fracture toughness in pure mode I (GIc) and tensile cohesive strength ( σn0) of the two adhesives were initially determined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively. Particular emphasis was given to GIc, as this is the most influent parameter for the numerical predictions. The numerical simulations of the DCB tests with the proposed laws matched accurately the experimental load–displacement (P–δ) curves, which validated the analysis procedure. The accuracy of the data reduction methods for calculation of GIc was checked by comparison of the input values in the simulations with the results of GIc calculations, with good results.

Simulation of debonding in Al/epoxy T-peel joints using a potential-based cohesive zone model

In this work, a cohesive zone model of fracture is employed to study debonding in plastically deforming Al/epoxy T-peel joints. In order to model the adhesion between the bonded metal strips, the Park-Paulino-Roesler (PPR) potential based cohesive model (J Mech Phys Solids, 2009;57:891-908) is employed, and interface elements are implemented in a finite element com-mercial code. A study on the influence of the cohesive properties (i.e. cohesive strength, fracture energy, shape parameter and slope indicator) on the predicted peel-force versus displacement plots reveals that the numerical results are mostly sensitive to cohesive strength and fracture energy. In turn, these parameters are tuned until a match between experimental and simulated load displacement curves is achieved.

Experimental and analytical study on the deformation response of closed-cell Al foam panels to local contact damage—Mechanical properties extraction

The present paper studies the deformation response of closed-cell aluminium foam panels (ALPORAS brand) to local contact damage, experimentally simulated by indentation tests with indenters of various shapes and sizes. The foam density varies between 0.184 g/cm 3 and 0.351 g/cm 3; panels of various thicknesses are also considered. Analytical models are developed to estimate the crushing force, the tearing resistance, and the shearing resistance in indentation with cylindrical and spherical indenters. Of particular interest are the failure mechanisms, the foam ligament tear energy and the foam shear strength in all indentation types. The tear energy, as well as the shear strength, is deduced by fitting the experimental load–displacement curves and using the developed analytical models. The influence of the panel thickness, indenter shape and size, and foam microstructure on the deformation mechanisms and material properties is also discussed.

Understanding formability of extra-deep drawing steel at elevated temperature using finite element simulation

Deep drawing involves conversion of flat thin sheet metal blanks into parts of desired shape. Although applications of deep drawing processes at elevated temperatures (warm forming) have not yet been used effectively nowadays, it is clear that it is going to be a very important manufacturing application in the future. Warm deep drawing process of circular blanks is investigated using a 20 T hydraulic press and a finite element model coupled with thermal analysis. The present work is aimed to investigate the limiting draw ratio (LDR) and the coefficient of friction of extra-deep drawing (EDD) steels at room temperature and at 200 °C. Simulation and experimental results showed an increase in the LDR as the temperature increases and the coefficient of friction was estimated by comparing the simulation and experimental load–displacement curve. Finite element simulation results were in good agreement with the experimental results.

Fracture characterization of sandwich structures interfaces under mode I loading

The accurate prediction of failure of sandwich structures using cohesive mixed-mode damage models depends on the accurate characterization of the cohesive laws under pure mode loading. In this work, a numerical and experimental study on the asymmetric double cantilever beam (DCB) sandwich specimen is presented with the objective to characterize the debonding fracture between the face sheet and the core under pure mode I. A data reduction method based on beam theory was formulated in such a way to incorporate the complex damaging phenomena of the debonding due to the material and geometric asymmetry of the specimen, via the consideration of an equivalent crack length ( a e). Experimental DCB tests were performed and the proposed methodology was followed to obtain the debonding fracture energy ( G Ic). The experimental tests were numerically simulated and a cohesive damage model was employed to reproduce crack propagation. An inverse method was followed to obtain the local cohesive strength ( σ u,I) based on the fitting of the numerical and experimental load–displacement curves. With the value of fracture energy and cohesive strength defined, the cohesive law for interface mode I fracture is characterized. Good agreement between the numerical and the experimental R-curves validates the accuracy of the proposed data reduction procedure.

Gurson-Tvergaard-Needleman parameters identification using artificial neural networks in sheet metal blanking

This paper presents a method for the identification of large used coupled damage model parameters in sheet metal blanking. The existing finite element models describe easily the elastoplastic behaviour occurring during the sheet metal blanking. However, the description of the damage evolution is much more delicate to appreciate. The proposed method connects finite element method (FEM) with artificial neural networks (ANN) analysis in order to identify the values of the Gurson-Tvergaard-Needleman (GTN) parameters. Blanking tests are carried out to obtain the experimental material response under loading. A finite element model is used to compute the load displacement curve depending on the GTN parameters. Via a full design of experiments, a numerical database is built up, which is used for the ANN training. The identification of the damage properties is done by minimizing the error between an experimental load displacement curve and a predicted one by the ANN function. The identified damage law parameters are validated on the other experimental configurations of blanking tests.

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.

Determination of cohesive parameters for a mixed-mode cohesive zone model

The mechanical behaviour and failure properties of adhesive joints are influenced not only by adhesive properties but also by interface characteristics. Various modelling methods have been proposed to predict the failure behaviour of adhesive joints. Among those methods, cohesive zone modelling, which consists of introducing a cohesive law in the numerical models to reproduce the adhesive layer, is widely used to simulate the behaviour of adhesive joints. The cohesive parameters of the traction–separation laws in each pure mode should be determined for application of this technique. It is known that the cohesive parameters are affected by both adhesive properties and interface characteristics so, in most cases, these parameters are iteratively obtained by matching numerical results to experimental results. In this paper, a systematic procedure for the determination of the cohesive parameters is proposed by introducing an optimization technique (design of experiment and the kriging metamodel). The first step is to identify design variables affecting a response of a system. In this study, the cohesive parameters are selected as the design variables. Once the design variables are identified, design ranges or sampling ranges of the design variables are determined in order to result in a near optimal response with the determined sampling ranges. If the design variables and the sampling ranges are obtained then the design of experiment is performed to determine appropriate sampling points in the sampling ranges and a minimum number of simulations. Then, the load difference between numerical and experimental load–displacement results at several values of displacements are defined as an error, and the kriging metamodel, which surrogates the error, is constructed based on the sampling points. Cohesive parameters are determined by applying the numerical nonlinear optimization algorithm to minimize the error. The proposed procedure is applied to a co-cured Single Leg Bending (SLB) joint under mode I and mode II-dominant modes and the cohesive parameters are determined. From these parameters, the mixed-mode cohesive zone model is constructed and applied to the simulation of the co-cured SLB joint under varying mode-mixities. Simulation results are compared with the experimental results. It is shown that the failure behaviour of the SLB joint is well-described by using the mixed-mode cohesive zone model with the determined parameters.

Nanomechanics of rhenium wires: Elastic modulus, yield strength and strain hardening

We report on the mechanical properties of rhenium wires that range in diameter from 400 to 1000 nm under bending, using in situ atomic force microscopy measurements inside a scanning electron microscope combined with finite-element simulations. Load–displacement curves are obtained from elastoplastic bending of nanowires. The average values of the bending modulus and yield stress of nanowires are found to be about 437 and 25 GPa, respectively. Computational simulations have been carried out to fit a power-law strain-hardening model to the experimental load–displacement curves. This allowed the true stress–strain curves to be reconstructed for simple bending experiments.

On prediction of the strength levels and failure patterns of human vertebrae using quantitative computed tomography (QCT)-based finite element method

This paper presents an effective patient-specific approach for prediction of failure initiation and growth in human vertebra using the general framework of the quantitative computed tomography (QCT)-based finite element method (FEM). The studies were carried out on 13 vertebrae (lumbar and thoracic), excised from 3 cadavers with the average age of 42 years old. Initially, 4 samples were QCT scanned and the images were directly converted into voxel-based 3D finite element models for linear and nonlinear analyses. The equivalent plastic strains obtained from the nonlinear analyses were used to predict the occurrence of local failures and development of the failure patterns. In the linear analyses, the strain energy density measure was used to identify the critical elements and predict the failure patterns. Subsequently, the samples were destructively tested in uniaxial compression and the experimental load–displacement diagrams were obtained. The plain radiographic images of the tested samples were also examined for observation of the failure patterns. In continuation, the presence of osteolytic defects in vertebrae was simulated by creation of artificial cavities within 9 remaining samples using a computer numerical control (CNC) milling machine. The same protocol was followed for scanning, modeling, and destructive testing of these samples. A strong correlation was found between the predicted and measured strengths. Finally, a typical vertebroplasty treatment was simulated by injection of low-viscosity bone cement within 3 compressed samples. The failure patterns and the associated load levels for these samples were also predicted using the QCT voxel-based FEM.

Refined model of elastic nanoindentation of a half-space by the blunted Berkovich indenter accounting for tangential displacements on the contact surface

Elastic contact between a non-ideal Berkovich indenter and a half-space is investigated. The derived mathematical model of the contact allows for tangential displacements of the boundary points of the half-space. The tip of the blunted indenter is simulated as a smooth surface. The boundary element method is implemented in the model for numerical simulation of nanoindentation. The relative deviation function is introduced and calculated to quantify the influence of the tangential displacements on the load–displacement curves. A simple expression is derived for the impact of the tangential displacements on the values of the reduced Young’s modulus determined due to nanoindentation studies. The refined model was successfully applied to simulate the experimental load–displacement curves gained by elastic nanoindentations of flat LiF and KCl samples. Such values of the indenter bluntness (the varying parameter) were found that the simulated load–displacement curves coincided with those of the experimental data at displacements higher than 7.5 nm. The model neglecting tangential displacements gives slightly differing values for the parameter of the indenter bluntness.

Finite element analysis and experimental investigation of the Hertzian assumption on the characterization of initial plastic yield

Sudden displacement excursions during load-controlled nanoindentation of relatively dislocation-free surfaces of metals are frequently associated with dislocation nucleation, multiplication, and propagation. Insight into the nanomechanical origins of plasticity in metallic crystals may be gained through estimation of the stresses that nucleate dislocations. An assessment of the potential errors in the experimental measurement of nucleation stresses, especially in materials that exhibit the elastic–plastic transition at small indentation depths, is critical. In this work, the near-apex shape of a Berkovich probe was measured by scanning probe microscopy. This shape was then used as a “virtual” indentation probe in a 3-dimensional finite element analysis (FEA) of indentation on 〈100〉-oriented single-crystal tungsten. Simultaneously, experiments were carried out with the real indenter, also on 〈100〉-oriented single-crystal tungsten. There is good agreement between the FEA and experimental load–displacement curves. The Hertzian estimate of the radius of curvature was significantly larger than that directly measured from the scanning probe experiments. This effect was replicated in FEA simulation of indentation by a sphere. These results suggest that Hertzian estimates of the maximum shear stresses in the target material at the point of dislocation nucleation are a conservative lower bound. Stress estimates obtained from the experimental data using the Hertzian approximation were over 30% smaller than those determined from FEA.

Pure mode II fracture characterization of composite bonded joints

A new data reduction scheme is proposed for measuring the critical fracture energy of adhesive joints under pure mode II loading using the End Notched Flexure test. The method is based on the crack equivalent concept and does not require crack length monitoring during propagation, which is very difficult to perform accurately in these tests. The proposed methodology also accounts for the energy dissipated at the Fracture Process Zone which is not negligible when ductile adhesives are used. Experimental tests and numerical analyses using a trapezoidal cohesive mixed-mode damage model demonstrated the good performance of the new method, namely when compared to classical data reduction schemes. An inverse method was used to determine the cohesive properties, fitting the numerical and experimental load–displacement curves. Excellent agreement between the numerical and experimental R-curves was achieved demonstrating the effectiveness of the proposed method.

Near surface mounted CFRP strips for the flexural strengthening of RC columns: Experimental and numerical research

In this work, a strengthening technique based on near surface mounted (NSM) carbon fibre laminate strips bonded into slits opened on the concrete cover is used to improve the flexural capacity of columns subjected to bending and compression. This technique avoids the occurrence of the peeling phenomenon, is able to mobilize the full strengthening capacity of the strips, and provides higher protection against fire and acts of vandalism. We describe the adopted strengthening technique and report the experimental characterization of the materials involved in the strengthening process. The results obtained in two series of reinforced concrete columns, subjected to axial compression and lateral cyclic loading, show that a significant increase on the load carrying capacity can be achieved by using the NSM technique. Cyclic material constitutive laws were implemented in a finite element program and the tests with reinforced concrete columns strengthened with the NSM technique were numerically simulated under cyclic loading. These numerical simulations reproduce the experimental load–displacement diagrams satisfactorily.

Computational modelling of dissipative open-cell cellular solids at finite deformations

This study concerns the constitutive modelling of dissipative open-cell structural cellular solids under primarily finite compressive deformations and the corresponding non-linear finite element implementation. A thermodynamically consistent, mechanistic approach presented in Hård af Segerstad et al. [Hård af Segerstad, P., Larsson, R., Toll, S., 2008. A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy. International Journal of Plasticity. 24, 896–914.] is adopted for modelling the initial linear-elastic response and the subsequent plateau behaviour. In these regions the cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is further assumed to be one-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz, the introduction of multiple non-linear mechanisms, such as hyperelasto-viscoplasticity and damage becomes feasible for large scale computations. An additional hyperelastic volumetric response, activated near the point-of-compaction, is introduced for two reasons, (i) to capture the stiffness recovery at high compressive volumetric deformations, where the struts come into contact, and (ii) to prevent numerical instability. The model is implemented as a user defined constitutive driver in the implicit version of the finite element code ABAQUS and tested experimentally for an open-cell aluminium alloy foam (Duocel 6101-0, 40 ppi). All material parameters are determined by a simple compression test, and subsequently used to simulate the indentation of a rigid sphere into a foam cylinder. The model accurately captures the experimental load–displacement relation and the deformed geometry.

Mechanical modelling of indentation-induced densification in amorphous silica

Despite their brittleness, silicate glasses undergo plastic deformation at the microscopic scale. Mechanical contact and indentation are the most common situations of interest. The plasticity of glasses is characterized not only by shear flow but also by a permanent densification process. After indentation, densification can locally reach 20% in a pure silica glass. In this paper, a new constitutive model, derived from experimental observations, is presented to account for the plasticity of fused silica. The use of nanoindentation tests to identify the plastic behaviour of amorphous silica is discussed. A set of material properties is determined by comparing experimental load–displacement indentation curves to the results of finite element simulations. The numerical results show good agreement with recent experimental indentation-induced densification maps obtained by Perriot et al. [Perriot A, Vandembroucq D, Barthel E, Martinez V, Grosvalet L, Martinet Ch, et al. J Am Ceram Soc 2006;89:596].

Investigation of material properties of thin copper films through finite element modelling of microindentation test

Technology processes of thin metal films deposition are entailed with changes in material’s microstructure. As a result, deposited films often are characterized with material properties, which are different from these of the original bulk material. Determination of these material characteristics is of big importance for practice. In the present work the material properties of thin bright copper film with known depth were investigated. The film was deposited electrochemically over substratum composed of metallurgic brass alloy (CuZn36). Based on the results from microindentation test the load–displacement curve is obtained after the indenter is unloaded and the imprint diameter is measured. Consequently the process of indentation was modelled numerically. The numerical simulation is based on the finite element model of the indentation process. As a result of the simulation the load–displacement curve was obtained numerically for a certain set of material parameters. The trial–error approach is applied to find most appropriate set which fit the experimental load–displacement curve. At the end results, which were obtained through numerical simulation give good coincidence with the experiment. Therefore the proposed method can be successfully applied for identification of material parameters of the accepted model. The proposed trial–error approach is appropriate for investigation of thin films with known thickness, deposited on a substrate with known material characteristics.

Incidence of nanoscale heterogeneity on the nanoindentation of a semicrystalline polymer: Experiments and modeling

The nanoindentation of semicrystalline polyamide 6 (PA6) specimens was evaluated by atomic force microscopy with an extremely sharp diamond tip whose apex was nominally less than 10 nm in radius. Nanoindentation was performed under dry and wet conditions on PA6 samples injection-molded at different melt temperatures. The bulk Young’s modulus of dry PA6 was found to be in good agreement with the literature, thereby confirming the experimental approach developed in this study. A major finding is the observation of sudden increases in force during the loading portion of the experimental load–displacement curves, which occurred regardless of water absorption. We also found some irregularity in the pile-up morphology around the indents, linked to the heterogeneous nature of the deformation in PA6. Finite element analysis was used to elucidate the phenomenon of force discontinuity by independently considering the variations in elasticity, yield stress and friction coefficient of the crystalline lamellar aggregates in PA6. It is shown that force discontinuities in nanoindented PA6 result from local differences in yield phenomena at the lamellar level. The present investigation sheds some light on the importance of mechanical heterogeneity emerging from contact interactions between an extremely sharp tip and the nanoscale morphology of semicrystalline polymers.