Experimental Load Displacement Research Articles

On the application of FEM to deformation of high-density polyethylene

This paper presents a study that uses finite element method (FEM) to simulate deformation behaviour of high-density polyethylene (HDPE) when subjected to tensile loading, either without or with the presence of pre-cracks. For the former, dog-bone-shaped model of HDPE was deformed under uni-axial tensile (UT) loading beyond the initial yielding, to generate stable necking in the gauge section. The paper proposes a simple correction factor to determine the equivalent von Mises stress that is needed for the input to the FEM model, in order to generate the same loading level as that observed experimentally for neck propagation. The paper points out that such consistency in the loading level could not be generated in the past mainly because of a misconception that axial stress in the neck was regarded as the equivalent of the von Mises stress. The study also explored the consideration of crack growth in double-edge-notched tensile (DENT) specimen, and showed that the conventional von Mises yield function, with the assumption of isotropic work hardening, cannot be directly applied to simulate the deformation behaviour of DENT specimen. Instead, empirical parameters were employed to reflect the polymer orientation during the necking process. The paper shows that FEM models for both UT and DENT tests can reproduce the experimental load–displacement curves quite accurately, and concludes that with a proper yield function to reflect the deformation involved in the mechanical tests, the deformation behaviour observed experimentally can be accurately mimicked using the FEM simulation.

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50–50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.

Enhancement of the flexural performance of retrofitted wood beams using CFRP composite sheets

The main objective of this study was to investigate the flexural performance of wood beams retrofitted by using carbon fiber reinforced plastic (CFRP) composite sheets. First, a theoretical analysis of wood beams retrofitted with CFRP composite sheets was derived. The four-point bending test was then used to determine the load–displacement relationships of wood beams. The performance of the CFRP sheets adhered to the tensile side of two different species of wood beams was investigated. Observations of the experimental load–displacement relationships show that flexural strength increased and middle vertical displacement decreased for wood beams retrofitted with CFRP composite sheets, compared to those without CFRP sheet. The increased percentages of flexural strength for the retrofitted Cunninghamia lanceolata with 1, 2 and 3 layers of CFRP composite sheets were 39%, 44% and 61%, respectively. The increased percentages of flexural strength for the retrofitted Tsuga chinensis with 1, 2 and 3 layers of CFRP composite sheets were 44%, 55% and 58%, respectively. Comparisons of the theoretical and experimental ultimate loads show the absolute errors of the ultimate load for C. lanceolata and T. chinensis to be 5.05% and 8.65%, respectively.

Material characterization at high strain rate by Hopkinson bar tests and finite element optimization

In the present work, dynamic tests have been performed on AISI 1018 CR steel specimens by means of a split Hopkinson pressure bar (SHPB). The standard SHPB arrangement has been modified in order to allow running tensile tests avoiding spurious and misleading effects due to wave dispersion, specimen inertia and mechanical impedance mismatch in the clamping region. However, engineering stress–strain curves obtained from experimental tests are far from representing true material properties because of several phenomena that must be taken into account: the strain rate is not constant during the test, the specimen undergoes remarkable necking, so stress and strain distributions are largely non-uniform, and the temperature increases because of plastic work. Experimental data have been post-processed using a finite element-based optimization procedure where the specimen dynamic deformation is reproduced. Optimal sets of material constants for different constitutive models (Johnson–Cook, Zerilli–Armstrong and others) have been computed by fitting, in a least mean square sense, the numerical and experimental load–displacement curves.

Performance of nonlinear degrading structures: Identification, validation, and prediction

The lack of a fundamental theory of hysteresis is a major barrier to successful design of structures against deterioration associated with earthquakes, high winds, and sea waves. Development of a practical model of degrading structures that would match experimental observations is an important task. This paper has a twofold objective. First, a superior system identification algorithm is devised to estimate the unspecified parameters in a differential model of hysteresis from experimental load–displacement traces. This algorithm is based upon the latest theory of genetic evolution and it will be streamlined through global sensitivity analysis. Second, the utility of identification of hysteresis is demonstrated through nonlinear response prediction, which is important in structural design. Suppose a hysteretic model is generated with a given load–displacement trace. It will be shown experimentally that the model will predict the response of the same system driven by other cyclic loads. The requirements for accurate prediction will be addressed. Through identification of hysteresis, it becomes possible to assess, for the first time in analysis, the performance of a real-life structure that has previously been damaged. In the open literature, there is not any other method that can perform the same task.

Comparison of fracture properties of two wood species through cohesive crack simulations

In the present work fracture (Mode I) was induced through three point-bending tests in two wood species used in timber construction: Maritime pine ( Pinus pinaster Ait.) and Norway spruce ( Picea abies L.). Load–displacement curves were experimentally determined and corresponding Resistance-curves ( R-curves) obtained using an equivalent linear elastic approach. An inverse method is presented to identify cohesive crack properties of a cohesive crack bilinear model used to simulate fracture in both wood species, combining experimental data and a developed genetic algorithm. Good agreement between numerical and experimental load–displacement and R-curves was obtained. Conclusions are drawn from finite element simulations regarding the extent of the numerical cohesive zone computed for each studied wood.

Seismic safety of structures: Influence of soil-flexibility, asymmetry and ground motion characteristics

Structures may experience degradation in strength in the event of strong seismic shaking. A rational estimation of the reserve strength of the structures is often desired in the process of retrofitting or strengthening the same. To achieve this end, the present paper confirms the suitability of an existing hysteresis model in reproducing experimental load–displacement characteristics for reinforced concrete ( R/C) structural members. Attempt has also been made for rational and realistic estimation of the degradation parameter required for the model in absence of any case-specific calibrated value. Subsequently, post-earthquake behaviour of the low-rise symmetric structures is assessed with and without accounting for the effect of soil–structure interaction. Such response for low-rise multistorey systems with regular asymmetry has also been investigated in the sample form. To develop insight into the behaviour of asymmetric (uni-directional and bi-directional) systems, detailed investigation has been made on idealized single-storey asymmetric systems under simulated and real ground motions with different phase difference or time lag variation. This suggests a serious implication of occurrence of peaks of the ground motions on the seismic performance of bi-directionally eccentric structures and indicates a relatively higher torsional vulnerability of bi-directionally eccentric system compared to equivalent uni-directional counterpart. The results along with the endeavour toward measuring the ductility capacity for R/C structural members based on the systematic observation and interpretation of the available experimental results, made in the paper, may prove useful in evaluating the seismic safety of low-rise R/C structures.

An upper-bound approach for equal channel angular extrusion with circular cross-section

Abstract In the present work, for the first time, an upper-bound approach is used to analyze the equal channel angular extrusion with circular cross-sections. Based on this model the power dissipated on all frictional and velocity discontinuity surfaces are determined and the total power optimized analytically. To compare the theoretical results with experiments, an ECAE die with a circular cross-section, having sharp corner was used to determine experimental extrusion force. The developed model predicts that the size of the plastic deformation zone and the relative extrusion pressure increase with increasing the constant friction factor. In addition the results show that there is a good agreement between the theoretical and experimental load displacement curve.

A procedure to prevent pile up effects on the analysis of spherical indentation data in elastic–plastic materials

Indentation tests are commonly applied to determine surface mechanical properties of very different kind of materials. In many circumstances, results provided by indentation are different to those obtain by more traditional tests (tensile, compression, etc.). In the particular case of elastic–plastic solids, phenomena like pile up or sink in cause deviations in Young’s modulus and hardness data if any correction procedure is applied to the experimental load–displacement curves. In this work, a finite element model was used to evaluate the pile up and sink in effects on the determination of mechanical properties in a wide range of elastic–plastic materials. Several combinations of Young’s modulus, yield stress and hardening exponent were considered. Taking into account the non-geometrical similarity of spherical tips, this configuration was chosen to suggest a new procedure, based on a combination of results obtained from tests performed at multiple maximum loads. The method gives consistent results and it was experimentally validated comparing nano-indentation and tensile tests of bulk metallic materials.

Sensitivity of polymer nanoindentation creep measurements to experimental variables

Spherical indentation creep experiments were used to characterize the viscoelastic response of three polymeric materials with different elastic and viscoelastic responses. A hereditary integral formulation for creep following ramp loading was used to analyze experimental indentation data. A wide range of conditions, including different load levels and ramp times, were employed to examine sensitivity of results to the selected experimental variables. Modulus values for materials exhibiting minimal time-dependent responses were found to agree well with known values and to be invariant of experimental conditions. However, a material with substantial time-dependent deformation in the experimental time frame was found to exhibit some effect of both load level and ramp time on modulus values. Time constants measured in the experiment varied with loading rate for two of three polymeric materials examined, but time constants did not vary with peak load. The examination of the shape of experimental load–displacement responses demonstrated no appreciable plasticity in two of three materials – the same two materials with both time- and level-independent creep responses.

소형펀치 시편을 이용한 원자력 재료의 파괴저항곡선 예측

Elastic-plastic fracture mechanics is popularly used for integrity evaluation of major components, however, it is not easy to extract standard specimens from operating facility. This paper examines how ductile fracture toughness is characterized by a small punch testing technique in conjunction with finite element analyses incorporating a damage model. At first, micro-mechanical parameters constituting Rousselier model are calibrated for typical nuclear materials using both estimated and experimental load-displacement (P-?) curves of miniaturized specimens. Then, fracture resistance (J-R) curves of relatively larger standard CT specimens are predicted by finite element analyses employing the calibrated parameters and compared with corresponding experimental ones. It was proven that estimated results by the proposed method using small punch specimen is promising and might be used as a useful tool for ductile crack growth evaluation.

A numerical study of factors affecting the characterization of nanoindentation on silicon

In this paper, the responses of nanoindentation on bulk silicon were investigated using finite element analysis. A two-dimensional finite element model under the assumption of axisymmetry was successfully validated by the experimental load–displacement curve. Four factors: coefficient of friction, indentation depth, tip rounding and indenter geometry were investigated to characterize the induced responses of bulk silicon via load–displacement curve, indentation surface profile at the maximum loading depth, residual surface profile after unloading, plastic energy, elastic energy, Young's modulus, hardness, and elastic recovery. Coefficients of friction were found to be insignificant, but the von Mises stress distributions after unloading between frictionless and frictional surfaces, indentation depth, tip rounding, and indenter geometry all showed having a distinct effect on stress, plastic energy, elastic energy, Young's modulus, hardness, elastic recovery and surface profile. The degree of pile-up affecting the investigated factors is discussed as well.

Experimental and numerical study of optimum die profile in backward rod extrusion

The aim of this research is the reduction in deformation load in backward rod extrusion by means of an optimum die profile. In this respect, the stress and load relations in this process have been obtained by the incremental slab method for a curved die profile. By the use of a computer program, the optimum die profile has been obtained on the basis of minimisation of stress and load in die-workpiece contact surface. By using the FEM software, ABAQUS, the optimum die angle for the conical die in the same conditions is also determined. Then, the finite-element and experimental load–displacement curves have been determined. It is illustrated that the extrusion load for optimum curved die is reduced by 11%, compared to that in the optimum conical die.

On system identification and response prediction of degrading structures

All structures degrade when acted upon by cyclic forces associated with earthquakes, high winds, and sea waves. Identification and prediction of degradation is thus a problem of considerable practical significance in the field of engineering mechanics. Under cyclic excitation, degradation manifests itself in the evolution of the associated hysteresis loops. Two principal tasks in connection with hysteretic evolution are addressed in this paper. First, a robust identification algorithm is devised to generate hysteretic models of a deteriorating structure from its experimental load–displacement traces. This algorithm is based upon the generalized Bouc–Wen model and the latest theory of differential evolution, streamlined through global sensitivity analysis. It can account for strength degradation, stiffness degradation, and pinching characteristics in the evolution of hysteretic traces. Second, it is shown experimentally that a hysteretic model obtained by identification can be used to predict the future performance of a degrading structure. Prediction of degradation through identification is a brute-force approach that offers a close representation of reality. There is not any method based upon the fundamental postulates of mechanics that can predict the response of a degrading structure well beyond its linear range. Copyright © 2005 John Wiley & Sons, Ltd.

Identification of ductile damage and fracture parameters from the small punch test using neural networks

This paper presents a method for the identification of deformation, damage and fracture properties of ductile materials. The small punch test is used to obtain the material response under loading. The resulting load displacement curve contains information about the deformation and failure behavior of the tested material. The finite element method is used to compute the load displacement curve depending on the parameters of the Gurson–Tvergaard–Needleman damage law. Via a systematic variation of the material parameters a data base is built up, which is used to train neural networks. This neural network can be used to predict the load displacement curve of the SPT for a given material parameter set. The identification of the material parameters is done by using a conjugate directions algorithm, which minimizes the error between an experimental load displacement curve and one predicted by the network function. The identified material parameters are validated by independent tests on notched tensile specimens. Furthermore, these parameters can be used to compute the crack growth in fracture specimens, which finally leads to a prediction of classical fracture toughness parameters.

Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y 0 and tangent modulus E T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point ( ε c, σ c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ c at the specific true strain ε C lead to the same loading and unloading indentation curve. We show that the true strain ε c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ c/ ε c is directly related to the elastic modulus of the indented material and the tip geometry.

Experimental and numerical study of optimal die profile in cold forward rod extrusion of aluminum

In this paper, the effect of die profile on the variation of stress and load in the cold forward extrusion of aluminum has been studied. The aim of this research is the reduction in deformation load, improvement in the metallurgical properties of the product and increasing in the die life by means of an optimum die profile. In this respect, the stress and load relations in forward rod extrusion for curved profiles have been obtained by using the slab method. In addition, by using a developed computer program, the optimum die profile has been obtained considering work hardening of the material in cold extrusion, on the basis of minimization of stress and load in die–workpiece contact surface. The obtained profile depends on the extrusion ratio, material properties of the workpiece and coefficient of friction which are the input parameters to the program. By using the finite-element software, ABAQUS, the optimum die angle for the conical die in the same conditions is determined. Furthermore, the finite-element and experimental load–displacement curves have been determined. The obtained results illustrate that the cold extrusion load for aluminum in the optimum curved die is considerably reduced, compared with that in the optimum conical die.

Nature of contact deformation of TiN films on steel

Nanoindentation experiments were carried out on a columnar ∼1.5-μm-thick TiN film on steel using a conical indenter with a 5-μm tip radius. Microstructural examination of the contact zone indicates that after initial elastic deformation, the deformation mechanism of the TiN is dominated by shear fracture at inter-columnar grain boundaries of the TiN film. A simple model is proposed whereby the applied load is partitioned between a deforming TiN annulus and a central expanding cavity in the steel substrate. It is possible to obtain a good fit to the experimental load–displacement curves with only one adjustable parameter, namely the inter-columnar shear fracture stress of the TiN film. The implication of results in the context of the performance of TiN films in service is also discussed.

Determination of Ductile Material Properties by Means of the Small Punch Test and Neural Networks

This paper compares two different methods for the identification of ductile properties of materials using the small punch test to measure the material response under loading. The finite element method is used to calculate the load displacement curve of the punch depending on the parameters of a hardening law. Via systematical variation of the material parameters a data base is built up, which is used to train neural networks. The second method allows the indentification of material parameters by using a conjugate directions algorithm, which minimizes the error between an experimental load displacement curve and one calculated by the network function.

J-R curve determination using the load separation parameter S pb method for ductile polymers

It is common practice to measure the fracture toughness of ductile polymers by the incremental crack growth resistance curve, where J is plotted as a function of crack extension. This article examines the applicability of a simple alternative methodology which has the inherent advantage of inferring the crack extension by comparing two experimental load displacement records obtained from a precracked and a blunt notched specimen. This methodology is based on the variable separability property, and on the assumptions that the load is independent of the crack growing history and it falls in correspondence with stable crack propagation. The separation parameter, S p b , is defined as the load ratio of a precracked and a blunt notched specimen. Its constancy identifies which points of the load displacement record have the initial crack length, while its variation is related to the onset of crack extension. From the S pb expression it is simple to obtain an equation from which to estimate the crack length using some predetermined calibration points. The methodology has been assessed in several commercial grade polymers, ABS, MIPS and thermally treated PP. Good agreement was found between the standard multiple specimen technique and the S pb method. In addition, a comparison was made with the single specimen normalization method.