Mechanical Behaviour Law Research Articles

Deep Drawing of Ti6Al4V: Experiments and Modeling over a Wide Range of Strain Rates and Temperatures

A combined experimental-numerical approach using digital image correlation (DIC) and finite element simulation in order to get the temperature dependent mechanical behaviour is presented. Results from a series of experiments on a Ti6Al4V titanium alloy sheet are shown. Tensile tests were carried out on specimens along 3 different orientations in order to characterise the material anisotropy. The strain-rates are varied from 10-1 to 10-2 s-1 while observations are made at temperatures from 903 to 1003 K. The samples are heated by Joule effect, which allows to use the image correlation in order to obtain the deformation fields and thus the coefficients of Lankford [1]. Differences in the responses of this alloy are observed in terms of work hardening, strain rate and temperature sensitivities. The Norton-Hoff model and the Hill [2] criterion are used to effectively simulate the observed responses obtained from these experiments. An inverse analysis model using kriging meta-model [3] is applied to determine each parameter of the mechanical behaviour law. The model, with the constants determined from these experiments, is then used to predict the mechanical behaviour of Ti6Al4V. Thus, the model is implemented into the implicit finite element code Forge® to model forming of thin-walled structures. The predictions are found to be very close to the observations.

Simulation of the thermomechanical and metallurgical behavior of steels by using ABAQUS software

Simulation is a very helpful and valuable work tool in the field of heat treatment of steels. It allows behavior laws and algorithms to be learned and tested. Simulation provides a low cost, secure and fast analysis tool. For a fine assimilation of the microstructure and distortion evolution concepts which characterize the surface hardening process, a simulation of the thermo-metallurgical and mechanical coupling is elaborated by using ABAQUS software linked to phase transformation and elastic–plastic modules which we developed taking into account of interactions between these fields. The application of this method makes it possible to highlight the metallurgical and mechanical behavior laws and procedures used to calculate phase fractions, austenite grain size, hardness, microstructure effect on physical properties, transformation latent heat, deformation progress, and stress genesis during a surface hardening; which cannot be feasible by using standard software based simulation. Predicted thermo-metallurgical results and residual stress have been compared with measured ones; the coincidence between simulated and experimental values confirms the validity of the chosen simulation tool.

Chemo-Mechanical Modeling Requirements for the Assessment of Concrete Structure Service Life

This paper deals with the formulation requirements for the finite-element modeling of the life cycle of concrete structures subjected to chemical evolution combined with mechanical loading. In particular, it considers the coupling of chemical evolution with nonlinear mechanical behavior combining creep and damage. Not only do the parameters of the mechanical model have to be adapted to the effect of chemical evolution, but also the chemical effects on the internal mechanical state variables of the chemical evolution have to be carefully considered. These two couplings are discussed and clarified in a general formulation useful for a finite-element implementation of a mechanical behavior law intended for chemo-mechanical applications. The approach is illustrated through a model developed to assess the mechanical behavior of concrete structures subjected to hydration and then to leaching during their service life. Hydration and leaching need to be considered together in the same model to study how damage of the concrete at its early age can affect its response in the long term. The model is implemented in a finite-element code and applied, first to the simulation of an early age creep test and then to the prediction of the very-long-term mechanical behavior of a nuclear waste storage facility.

Experimental and Numerical Analysis of Behaviour of Old Brick Masonries

The calculation of old existing masonry structures needs a homogeneous mechanical behaviour law under tensile and compressive load until collapse. The samples extracted from existing buildings are necessarily limited in dimension and number and it is not possible to perform tests directly on a representative volume, so the numerical modelling of masonry mechanical behaviour has to be predicted from the behaviour of its constitutive elements. The aim of the study presented here was to develop a method able to define the homogeneous representative law for brick masonry from those of its components, bricks and mortar, in tension and in compression, including linear and non-linear domains. The method is numeric, fitted on experimental results. Tests were carried out on mortar samples, brick samples, and multilayer samples. Their experimental behaviour is described and a damage model is used to describe the behaviour of the masonry. An explanation is given of how the homogeneous characteristics of the masonry were defined and the influence of some parameters is presented.

Spongy bone deformation mechanisms

In the fields of safety, ballistic protections and other medical applications, the accurate material constitutive law of spongy bone is needed to carry out valid finite element analyses for injury prediction. The direct identification of bone mechanical behaviour law is not easy since it is a complex network of intersecting osseous spans (trabeculae), where the space in and around the trabeculae contains bone marrow and fluids. In order to identify the spongy bone's mechanical behaviour, we performed compression tests on cylindrical samples. Experimental results show important dispersions and an unexpected inverse strain rate dependency at low range of loading velocities. The origin of the dispersions can be attributed to the combination of the architecture effect and the mechanical properties variation of the constitutive material. In order to reduce these dispersion sources and to understand the inverse strain rate sensitivity, we used a controlled constitutive material to build new equivalent samples with the spongy bone's architecture. These equivalent samples were subjected to compression tests. Numerical simulations of compression tests on the same architecture have been carried out with FE models built from µCt data. The obtained results are compared in term of final sample shape and the evolution of the compression force. This strain rate dependency can not be explained only by architecture effect.

Mechanical study of polymers in scratch test

The numerical study of the scratch test on glassy polymers needs a well adapted mechanical behaviour law both viscoelastic and viscoplastic. To test different models, an algorithm which allows to assembly in series two models has been developped. In our cas, it is used to associate a viscoelastic model with viscoplastic one. The simulations carried out lead to some phenomenological results showing the importance to account for the time dependency of the stiffness modulus.

Identification of the spongy bone mechanical behavior under compression loads: numerical simulation versus experimental results

In the fields of crashworthiness, ballistic protections, and other medical applications, the accurate material constitutive law of spongy bone is needed to carry out valid finite element analyses. The direct identification of bone mechanical behavior law is not easy since it is a complex network of intersecting osseous spans (trabeculae), where the space in and around the trabeculae contains bone marrow and fluids. We propose in this work to overtake the bone geometrical dispersion by applying an inverse scheme identification method, based on the global mechanical response, correlated with the exact geometry. First step study was made on spongy bone cylindrical samples cut in beef ribs. Compression tests on these samples showed a large dispersion and suggested that the fluid effect can be neglected during the quasi-linear part of the mechanical response. The micro-architecture of each sample was acquired thanks to microcomputed tomography technique (μCT). After applying a threshold, we used the μCT data to build a micro-FE model of the spongy bone. This model is introduced in FE code in order to simulate quasi-static compression of the sample. An elastic plastic constitutive law is assigned to the spongy bone. An optimization procedure is then applied in order to identify the spongy bone's behavior. The optimization function is based on the global response (force versus displacement) of the sample. This procedure was repeated for different samples in order to obtain average spongy bone behavior.

A nonlinear elastic behavior to identify the mechanical parameters of human skin in vivo

Various analyses have been performed to identify the mechanical properties of the human skin tissue in vivo. They generally use different approaches and hypotheses (behavior laws as well as mechanical tests) and the obtained results are consequently difficult to analyze and compare. In this paper, an inverse method that can be adapted to any kind of mechanical tests and behavior laws is presented. A suction deformation performed on the volar aspect of the forearm of a subject is considered. This test is modeled with the finite element method to compare the experimental and simulated curves using an inverse method that allows the skin mechanical parameters identification. This process is based on two optimization algorithms, Kalman's filter and Gauss-Newton's methods. To account for the nonlinear behavior of the skin, a specific nonlinear elastic law, which is then compared with standard linear elastic and neo-Hookean's mechanical behaviors, was developed. The obtained results first prove that neither linear elasticity nor neo-Hookean's laws can be used to model the skin. On the contrary, the nonlinear elastic model presents a relevant fit of the experimental curves. The skin thickness is also proved to be another key point to be taken into consideration. The obtained results are successfully compared with literature and the reliability of the proposed method is underlined with the identification of 300 additional experimental curves. The different works we are currently focusing on are finally introduced.

A new constructive method using the theory of invariants to obtain material behavior laws

The aim of this paper is to present a constructive method to derive mechanical behavior laws using the Theory of Invariants and Continuum Thermodynamics. More precisely, we want to construct, in a general way, the state or dissipation potential in a polynomial form given a set of variables V and the material symmetry group S. For this purpose, we show how to obtain a set of generators for the S-invariant polynomials of V. Then, using the Grœbner basis concept, we write all the decompositions of a polynomial of a given degree.

Deformation of Granitic Rocks: Experimental Studies and Natural Examples

Crustal deformation is inherently complex because the crust is inhomogeneous and anisotropic on a wide variety of scales. Advances in our understanding have come from a combination of field observations, laboratory experiments and theoretical models. What necessarily links all these investigations is a focus on process. Crystal plasticity (dislocation creep) is one of several grain-scale deformation processes or mechanisms; each process is dominant over a certain range of conditions in the crust, has a particular form of the flow law, and produces a characteristic set of microstructures. Characterizing the deformation mechanisms for different minerals, over a range of conditions, allows one to link the mechanical behavior or flow law associated with that process to the microstructures it produces. The information on microstructures can be used to help interpret the thermomechanical history of naturally deformed rocks, and flow laws can be used to create more realistic models predicting crustal behavior in different tectonic settings. Iterations among field, theoretical, and experimental approaches are critical for making progress in our understanding. The deformation process of crystal plasticity is the main focus of this volume. Crystal plastic deformation of the crust is in many ways more complex than that of the mantle, because most crustal rocks are polyphase aggregates, and the strengths of common crustal silicates (such as quartz, feldspar, and mica) are very different at a given set of conditions. Yield strength envelopes for the crust, as shown schematically in Figure 1⇓, are commonly plotted using the dislocation creep flow law for quartz, which inherently assumes that quartz is the controlling phase and undergoes steady state flow. But is the flow law for dislocation creep of quartz a good approximation for the deformation of a granite, let alone a crustal ‘plum pudding’ of regions and layers of different lithologies? The crust …

Influence of the mechanical behavior law on the drying of an alumina gel

Some catalysts supports are made from gelified alumina pellets. In the manufacturing process, drying can be an important stage in improving both texture and strength. In order to ease the comprehension of the phenomena, the drying of a pellet has been modeled with an Eulerian set of conservation equations (mass, energy and motion). A pseudo-elastic law issued from rheological experiments has been used to close the mechanical problem.

Investigation of 3-D mechanical properties of blood vessels using a new in vitro tests system: results on sheep common carotid arteries.

In order to investigate the three-dimensional (3-D) mechanical properties of blood vessels, a new experimental device is described allowing in vitro static and dynamic measurements on segments of arteries with high technical performances. Static tests are applied to sheep common carotid arteries. Considering a thick-walled cylindrical model of orthotropic material under large deformations, a classical 3-D approach based on strain energy density is used to calculate the resulting mechanical behavior law in radial and circumferencial directions and stresses distribution throughout the wall thickness. Results are presented with reference to unloaded and zero-stress initial state thanks to simple measurements of inner and outer circumferences. A particular ratio relating the two main stresses (circumferential and longitudinal) is calculated that put into the forth the progressive modifications in the direction of the predominant stress in the wall and the specific radial location where these changes occur. We observe that this point location is a function of the test conditions of the specimen, i.e., stretching length and level of pressure.

Characterization of Mechanical Properties in Surface-Treated Materials

Abstract An experimental methodology was developed for identification of mechanical behavior laws, in which the evolution of the stresses and strains in the surface of the samples is determined by X-ray diffraction and electric resistance strain gages, respectively, as a function of the loading in four-point bending tests. The determined stress-strain curve is then characteristic of the near-surface layers of the samples. The method was validated for different steels by comparing the results of samples with homogeneous properties on the cross section with the results of tension tests. The developed methodology was applied to the study of steel samples submitted to surface treatments, presenting gradients of chemical composition, microstructure, and mechanical properties from the surface to the bulk material.

Mechanical behaviour of brittle cement grains

Before attempting a modelling approach to the crushing mechanisms of “cement clinker” it was necessary to characterize the mechanical behaviour of this material up to breakage. The diametrical compressive test was chosen, as it is the closest to the typical loading within a packing of grains and a very convenient experimental approach for the analysis of mechanical behaviour law up to fragmentation of brittle granular material. The modellization of the grain as a hard brittle core surrounded by a thin crumbly skin leads us to associate the contact setting with the crumbly skin behaviour and the breakage with the brittle core behaviour. This analysis allowed us to define scaling laws for the skin thickness and breakage load. The breakage force increases as a power law of the grain diameter with an exponent of 1.5 and it is shown that the mean prefactor K0 is an intrinsic characteristic parameter proportional to the tenacity of the material.

On thermo-elastic-viscoplastic analysis of cooling processes including phases changes

This paper deals with the modelling and calculation of thermal, metallurgical and mechanical phenomena which occur in the quenching of steels. Especially the influence of the mechanical behaviour law of the material, either thermo-elasto-plastic or thermo-elasto-viscoplastic, on the development of internal stresses during cooling is analysed using the specific case of cooling of a cylinder made of eutectoïd carbon steel.