Stress–strain curve | EPFL Graph Search

In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Definition
Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves. The stress and strain can be normal, shear, or mixture, and can also can be uniaxial, biaxial, or multiaxial, even change with time. The form of deformation can be compression, stretching, torsion, rotation, and so on. If not mentioned otherwise, stress–strain curve refers to the relationship between axial normal stress and axial normal strain of materials measured in a tension test.

Investigations and numerical modeling of mechanical properties of tempered martensitic steel Eurofer97 at various loading rates, temperatures and after spallation irradiation

Serafin Knitel

The reduced activation tempered martensitic steel Eurofer97 is a reference steel for a structural applica-tions in fusion reactors. The first-wall and blanket materials will be subjected to high thermal and neutron fluxes and will experience very complex, time-dependent mechanical loading. Owing to impinging neutrons in materials, points defects and gasesous impurities (hydrogen and helium) are created and accummulated in the form of small defect clusters in the microstructure altering the mechanical properties. Notably, fracture toughness decreases as strength increases. Eurofer97, being a body centered cubic alloy, presents a ductile-to-brittle transition temperature T0 that shifts to higher temperatures after irradiation. The main objective was to study the loading rate and irradiation effects on plastic flow and fracture properties of Eurofer97. Tensile and fracture tests were performed at temperatures in the transition region, at low and high loading rates on unirradiated material. Tensile properties of irradiated material were assessed after irradiation in the Swiss neutron spallation source SINQ to a dose of about 11 dpa and helium content of 500 appm at about 250 Â°C. The information gathered from the mechanical tests was used either as input in finite element models of fracture specimens, or as benchmark data to calibrate and verify the predictions of the models. Fractographic observations were also conducted. The tensile tests on unirradiated Eurofer97 showed a strong temperature dependence and strain rate sensitivity of the stress at low temperature, consistent with a mechanism of nucleation and propagation of double kink on screw dislocation. At high loading rate, the strain rate hardening was partially compensated by thermal softening due to quasi-adiabatic heating. The tensile properties after irradiation showed strong irradiation hardening (increase of the yield stress) accompanied by a drastic decrease of uniform elongation. The constitutive behavior at large strains, representative of those at crack tip, was obtained with an inverse method, based on finite element (FE) models of tensile specimens, developed to derive the true stress-strain curves from the load-displacement ones. These curves were used as input for the FE models of fracture specimens. Comparative fractographic observations on unirradiated and irradiated specimens did not reveal any strong effect of irradiation or helium on fracture mechanism, which remains transgranular cleavage. This observation indicates that higher helium concentration than 500 appm is necessary to initiate intergranular cleavage by helium bubble precipitation on grain boundaries. Dynamic fracture tests were performed on unirradiated Eurofer97. A shift of about 10 Â°C of T0 by one order of magnitude in loading rate was determined, which was in good agreement with results obtained on different ferritic steels. Static fracture toughness tests were also performed on disk compact tension specimens that can be accommodated in irradiation tubes of SINQ. Different FE models of fracture specimens were developed to include strain-rate sensitivity of flow stress, heating resulting from the plastic work in the fracture process zone and loading rate. The structure of the stress field at the crack tip was studied and the temperature dependence of a lower bound to toughness data in the transition was reconstructed using a calibrated criterion of local approach to brittle fracture.

EPFL2018

Deformation behavior of nanoporous polycrystalline silver layers sintered by low temperature bonding: experiment and simulation

Saba Zabihzadeh

Integrated circuit packaging technology has become a prime design consideration for the develop-ment of electronic system concepts. One key issue is the bonding layer between chip and substrate. Currently, high-lead solder materials are being used, which apart from their environmental problem, limit the reliable operation temperature of devices to temperatures lower than 175ºC. Low-temperature bonding by sintering nanograin sized silver is emerging as a promising replacement in power electronics modules working at high temperatures. Although silver has been studied as bonding material since three decades, it has not been widely used in the packaging industry which might be ascribed to the limited knowledge on its mechanical behavior. In this work, the microstructure of thin layers of nanoporous silver sintered under different conditions are studied and linked to the mechanical behavior (at room temperature) using X-ray diffraction in-situ deformation tests and finite element simulations. First the microstructure of several samples such as grain size distribution, defect structures, porosity, pore morphology and ligament size distribution are investigated and are related to the corresponding sintering conditions. Electron microscopy, high resolution X-ray imaging, and X-ray diffraction techniques are the employed characterization methods. We found a strong dependency of the microstructure on the sintering conditions. Afterward, series of X-ray diffraction in-situ continuous, load-unload and stress relaxation tensile tests are performed to study the deformation mechanisms at room temperature. All samples exhibit small elongation and a large hysteresis in the stress-strain curve. From the change in the peak position upon unloading the residual elastic strain inside the sample is calculated while the evolution of the peak broadening provides information on the recovery mechanisms and induced dislocations. A significant recovery in the peak position and peak broadening after unloading and during relaxation is observed for all specimens. This is attributed to the presence of the pores. We found that the density of generated dislocations during tensile deformation depends on the porous structure. The results suggest that there exist two contributions to deformation: one related to the pores and other to intra-granular dislocations. The competition between both mechanisms is discussed in terms of porosity and grain size. Finally, 3D FE microstructure-based simulations are performed to allow a better correlation between the porous morphology and mechanical behavior. The 3D reconstructed images of nanoporous silver obtained from X-ray ptychography are used as an input to create finite element meshes of the actual porous morphology. For homogenization purpose, a representative volume element approach is chosen. The apparent elastoplastic response of the bulk silver is extracted from the porous samples using inverse homogenization method. The simulations allow distinguishing between the interplay and role of the ligament size, pore morphology and porosity, and provide a better comprehension on the experimental observations. We show that the proposed model has a predictive character for general nanoporous silver microstructures.

EPFL2016

Capacité portante de ponts en arc en maçonnerie de pierre naturelle

Alix Grandjean

Historical masonry arch bridges are an integral part of our cultural heritage and deserve the attention and the efforts required to safeguard their patrimonial value. There is currently a diverse range of methods available to engineers for evaluating the load-bearing capacity of masonry arches. The major drawbacks are that these methods are either too conservative or computationally intensive. The study presented here proposes a model based on the theory of plasticity. The result is a transparent model that is both rapid and easy to use. Moreover, its application does not involve heavy computation tools. The model is validated by comparison with available experimental results and with the results of a widely-recognised analysis software. In order to take into account the material and structural behaviour of an arch in an optimal way, the present thesis provides a new integral model divided into three evaluation levels. At the micro-level, the response of masonry under pure compression is used to characterise the material of an arch. At this level, numerical models are used to describe the behaviour of natural-stone masonry. These models distinguish between the constitutive units and mortar as well as the unit – mortar interface. The shape and arrangement of the units have the most influential role in defining the failure mode in comparison to the properties of each constitutive material. At the meso-level, the material behaviour from the preceding level is used to define the limit for the local plastification of an arch section under combined compression and flexure. This phenomenon is described as the formation of a hinge. The resistance of an arch section can be expressed using the bending moment – normal force interaction diagram based on the stress-strain curve of the masonry material. Each point along the interaction diagram refers to a state of stress causing the local plastification of an arch section due to the formation of a hinge. The macro-level focuses on the structural analysis of a masonry arch – a structure with four degrees of indeterminacy. The arch failure corresponds to the successive formation of four hinges defined by the yielding condition determined at the meso-level. The analytical model developed in this study considers an arch at the state of being a statically determinate structure – after three of the four hinges are developed. Using the principle of equilibrium, the model calculates the load-bearing capacity of the arch at the ultimate limit state. A large number of existing natural-stone masonry arches include deficiencies accumulated throughout years of service without any regular maintenance. Three common types of deficiencies on these bridges are considered. The model is extended to take into account their effects on the load-bearing capacity of arches. Finally, the model developed in this study is incorporated into a global methodology for the examination of masonry arch bridges. This methodology implies two complementary approaches, which have to be applied parallel to one another. The first uses the developed model and gives a quantitative evaluation of structural security. The second includes a qualitative appreciation of the risk, based on the condition survey of the structure. This methodology allows an objective examination of the structure and recommendations for intervention measures.

EPFL2010