Design of heterogeneous mechanical tests: Numerical methodology and experimental validation

Standard material parameters identification strategies for constitutive equations generally use an extensive number of classical tests for collecting the required experimental data. Recently, new specimen geometries for heterogeneous tests were designed to enhance the richness of the strain field and capture supplementary strain states using full‐field measurement techniques. The butterfly specimen is an example of such a geometry, designed through a numerical optimization procedure where an indicator capable of evaluating the heterogeneity and the richness of strain information is used. The aim of this work is to experimentally validate the heterogeneous butterfly mechanical test in the parameter identification framework. Blanks of mild steel DC04 are cut with the butterfly geometry, and specific grips are designed. Tests are performed with Digital Image Correlation technique, and a Finite Element Model Update inverse strategy is used for the parameter identification, as well as the calculation of the indicator. The identification strategy is accomplished with the data obtained from the experimental tests, and the results are compared with quasi‐homogeneous tests.     

Simulation and Validation of Welding Residual Stresses Based on Non‐Linear Mixed Hardening Model

Abstract: This study contributes to Phase 2 of the Task Group 1 round robin in the NeT European Network. To obtain better prediction results, in the thermal analysis, two significant changes are used. The welding efficiency, η, is fixed at 75%, and the weld bead fusion boundary profiles are based upon macrographs taken from welded specimens, which have been destructively examined. In the subsequent mechanical simulation, a non‐linear kinematic or mixed isotropic–kinematic hardening model should be employed, and a progressive annealing scheme or explicit consideration of visco‐plastic or creep effects should be implemented to handle high‐temperature inelastic strains and reduce stress discontinuities. In this study, an uncoupled 3D thermal and mechanical analysis was carried out using the software code SYSWELD. In the thermal simulation, a two‐offset‐double‐ellipsoid heat source model was developed, and the parameters were fitted using the heat source fitting tool. Power intensity was applied to simulate 1‐s dwelling time at the weld start end. Offset distances between two double ellipsoids were adjusted to obtain the weld bead transverse fusion boundary profiles at different positions. Predicted temperatures were compared with the measured data by thermocouples on the test pieces. In the mechanical analysis, a new material constitutive model, non‐linear mixed hardening model, was developed. Tension–compression cyclic tests were simulated at different temperatures using three different material hardening models (isotropic hardening model, kinematic hardening model and non‐linear mixed isotropic–kinematic hardening model), and the predicted cyclic stress–strain curves were compared with the measured data. Effects of three different hardening models on the welding residual stresses were studied. Compared with the measured data, the optimum material hardening model was confirmed.     

Thermo-elastic material parameters identification using modified error in constitutive equation approach

This paper presents an identification procedure for anisotropic thermo-elastic heterogeneous material profile based on modified error in constitutive equation (MECE) approach. The inverse problem is posed as an optimization problem where the objective functional evaluates the difference in constitutive relation that associates kinematically admissible strain field to the statically admissible stress field. An additional term due to corruption in measurement data is included in the cost functional as a penalty form. While following standard MECE-based identification procedure, we have proposed a trace norm of the constitutive discrepancy functional that arises due to two dissimilar fields for material parameter update. In the process, we obtain explicit parameter update formula for general anisotropic thermo-elastic material. However, unlike elastic case, parameter update equations are nonlinear due to thermo-elastic constitutive relation. Finally, the potential of the proposed procedure in estimating anisotropic material parameters is illustrated through some large-scale parameter estimation problems.     

A Review of the Challenges and Limitations of Full‐Field Measurements Applied to Large Heterogeneous Deformations of Rubbers

Abstract: This paper presents an overview of the use of full‐field measurement techniques, more precisely digital image correlation (DIC) and coupled DIC and infrared thermography, for the material and structure characterisation of rubber reported in the literature. Even though such techniques have increasingly been applied for approximately 30 years for moderate deformations in metal and composite materials, they are still under‐employed in the measurement of full kinematic and thermal fields in the case of large deformations undergone by rubber materials. To date, the applications addressed are crack propagation at both macroscopic and microscopic scales, model validation and constitutive parameter identification.     

A general linear method to evaluate the hardening behaviour of metals at large strain with full‐field measurements

The hardening behaviour of metals is generally described in terms of a stress‐strain curve derived from experiments. In this paper, a linear method to identify the stress‐strain curve starting from full‐field measurement data is presented. This method can be applied to any stress state using a generic yield function, the only requirement is that the full‐field measurement is extended up to the border of the specimen. The method is presented and validated using a finite element model of a notched specimen. Moreover, experiments were performed on specimens cut from a BH340 steel sheet to illustrate the viability to actual cases. Two geometries were considered, a standard uniaxial test, where the method was used to evaluate the post‐necking behaviour, and a notched specimen with a heterogeneous strain field. The proposed method, named linear stress‐strain curve identification (LSSCI), can be a useful tool in combination with inverse methods to identify the constitutive behaviour of metals in large strain plasticity.     

Full-field measurement technique and its application to the analysis of materials behaviour under plane strain mode

The purpose of the paper is to provide a comprehensive experimental and numerical analysis of one of the encountered and critical state modes in sheet metal forming processes. The study is carried out with the help of the full-field measurement techniques. In order to confer some generality to the proposed work, several materials and different specimen shapes are considered that exhibit more or less homogeneous strain field. The proposed experimental study of the plane strain test is completed by a preliminary identification of the material parameters for non-linear behaviour at finite strains, using heterogeneous strain field.     

Measurement of thermal diffusivity of solids using infrared thermography

We report measurement of thermal diffusivity of solid samples by using a continuous heat source and infrared thermal imaging. In this technique, a continuous heat source is used for heating the front surface of solid specimen and a thermal camera for detecting the time dependent temperature variations at the rear surface. The advantage of this technique is that it does not require an expensive thermal camera with high acquisition rate or transient heat sources like laser or flash lamp. The time dependent heat equation is solved analytically for the given experimental boundary conditions. The incorporation of heat loss correction in the solution of heat equation provides the values of thermal diffusivity for aluminum, copper and brass, in good agreement with the literature values.     

Combined simulation?experimental approach to power cable thermal loading assessment

The performance of an underground transmission and distribution system is critically influenced by the thermal properties of the surrounding medium, as well as the thermal properties of the cable itself. The thermal behaviour of the cable is strongly dependent on the loading conditions and thermal parameters of the cable materials as well as the thermal characteristics of the surrounding soil, ambient environment and boundary conditions. A combined experimental- computational investigation is performed to examine the thermal parameters which may influence the performance of the underground cable. First, the thermal specification of the soil was tested by simulating a high temperature gradient along the body of the tested sample enclosed by a heat source-heat sink pair facing each other. In the second part, the 15 kV XLPE underground power cable is energised as a heat source as in the actual case. The thermal field at different spots and loadings was investigated using a developed full-size experimental setup to monitor the thermal behaviour of the underground cables, surrounding soil and boundaries phenomena (heat coefficient losses at the convective boundaries and the heat losses at the isolated boundaries). The proposed combined finite-element-gradient optimisation method is used to estimate the cable thermal parameters. This is based on matching the computational simulation of the experimental model based on finite element to that obtained from the experimental measurements.     

A 3D domain decomposition approach for the identification of spatially varying elastic material parameters

The post‐treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential of the constitutive compatibility method for tackling such an inverse problem, provided an appropriate domain decomposition technique is introduced. In the method described here, the statically admissible stress field that can be related through the known constitutive symmetry to the kinematic observations is sought through minimization of an objective function, which measures the violation of constitutive compatibility. After this stress reconstruction, the local material parameters are identified with the given kinematic observations using the constitutive equation. Here, we first adapt this method to solve 3D identification problems and then implement it within a domain decomposition framework which allows for reduced computational load when handling larger problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Mechanical design of a heterogeneous test for material parameters identification

The main goal of this work is to design virtually a heterogeneous test, with appropriate specimen shape and boundary conditions, which leads to an inhomogeneous strain field promoting the mechanical behavior characterization of thin metallic sheets under several strain paths and strain amplitudes. Finite element simulations were carried out with a virtual material, described by an anisotropic yield criterion (Yld2004-18p) associated to a mixed hardening law. The material parameters were derived from a large experimental database of quasi-homogeneous classical tests. A shape and boundary conditions optimization process was developed based on a quantitative indicator rating the strain field information and used as a cost function for guiding the test design. A heterogeneous test showing a butterfly shape was obtained, with strain states ranging from simple shear to plane strain tension. In addition, the designed heterogeneous test was used to determine the material parameters of the aforementioned constitutive model. The reliability of this identified material parameters set was then assessed and compared with the one coming from the experimental database composed by the quasi-homogeneous classical tests.     

High-Temperature Thermal Conductivity Measurement Apparatus Based on Guarded Hot Plate Method

An alternative calibration procedure has been applied using apparatus built in-house, created to optimize thermal conductivity measurements. The new approach compared to those of usual measurement procedures of thermal conductivity by guarded hot plate (GHP) consists of modified design of the apparatus, modified position of the temperature sensors and new conception in the calculation method, applying the temperature at the inlet section of the specimen instead of the temperature difference across the specimen. This alternative technique is suitable for eliminating the effect of thermal contact resistance arising between a rigid specimen and the heated plate, as well as accurate determination of the specimen temperature and of the heat loss at the lateral edge of the specimen. This paper presents an overview of the specific characteristics of the newly developed “high-temperature thermal conductivity measurement apparatus” based on the GHP method, as well as how the major difficulties are handled in the case of this apparatus, as compared to the common GHP method that conforms to current international standards.     

An improved comparative thermal conductivity apparatus for measurements at high temperatures

An apparatus developed for the measurement of thermal conductivity of solids at temperatures from 350 to 1250 K in air, vacuum, or any other controlled atmosphere is described. It is based on the steady-state axial heat flow comparative method and can be used for measurements of conductivities in the range 1 to 100 W·m^–1·K^–1. New heat source layout gives uniform heat flux across the specimen column, improving the accuracy of the measurements. The specimen stack is fixed in a rigid frame. It incorporates convection current breakers, eliminating thermal insulation of the stack and thereby considerably increasing the ease of specimen mounting. The accuracy of measurements was assessed by measuring the thermal conductivity of approved reference materials and is found to be within ±3%. The results of measurements on nickel of known purity are also presented. Error analysis of the system shows that the determinate error leaving the uncertainty in the thermal conductivity of the reference materials, is less than ±2%.     

Study on a Thermal-diffusivity Standard for Laser Flash Method Measurements

The National Metrology Institute of Japan (NMIJ) of AIST has been studying the laser flash method in order to establish an SI traceable thermal- diffusivity standard. Key technologies have been developed to reduce the uncertainty in laser flash measurements. In the present study, an uncertainty evaluation has been carried out on the laser flash measurement method in order to determine the thermal diffusivity value of IG-110, a grade of isotropic high-density graphite, as a candidate reference material. The thermal diffusivity measured by the laser flash method is derived from a specimen thickness and a heat diffusion time. And a laser flash measurement is carried out at a given temperature. The measurement system is composed of three sections corresponding to each measured quantity: length, time, and temperature. Therefore, we checked and calibrated our measurement system, and estimated the uncertainty of measurement results for the case of a grade of isotropic graphite.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Measurements of Thermal Diffusivity for Thin Slabs by a Converging Thermal Wave Technique

The measurement of thermal diffusivity for thin slabs by a converging thermal wave technique has been studied. Temperature variation at the center of the heat source ring that is produced by a pulsed high-power laser is detected by an infrared detector. A computer program based on the finite difference method is developed to analyze the thermal diffusivity of the slabs. Materials of both high thermal diffusivity (CVD diamond wafer) and low thermal diffusivity (stainless-steel foil) have been used for the measurements. The measurements have been performed by varying the size and the thickness of specimen. The converging thermal wave technique has proved to be a good method to measure the thermal diffusivity of a CVD diamond without breaking the wafer into small specimens. The technique can be applied for a small slab if the diameter of the slab is two times larger than that of the heat source ring. The sensitivity of thickness in measuring the thermal diffusivity is low for ordinary CVD diamond. The use of the converging thermal wave technique for nonhomogeneous, nonuniform, and anisotropic materials has been accomplished by applying the finite difference method.     

Conventional Simultaneous Measurement of Specific Heat Capacity and Thermal Conductivity by Thermal Radiation Calorimetry

Thermal radiation calorimetry has been applied to measure the thermal conductivity and the specific heat capacity of an isolated solid specimen simultaneously. The system, in which a disk-shaped specimen and a flat heater are mounted in a vacuum chamber with the specimen heated on one face by irradiation, is presented. A theoretical formulation of the simultaneous measurement at quasi-steady state is described in detail. Noncontact temperature measurement of both specimen surfaces has been performed using pyrometers and a thermocouple set in the gap between the heater and the specimen. Pyroceram 9609 specimens, whose surfaces were blackened with colloidal graphite, were used in the measurement. The largest error involved in the noncontact temperature measurement is ±2°C in the range from 450 to 650°C. The resultant values of the specific heat capacity and the thermal conductivity deviate by about 10% from the recommended values for the Pyroceram specimen.     

Thermal conductivity by a pulse-heating method: Theory and experimental apparatus

A new dynamic technique for the measurement of thermal conductivity at high temperatures has been developed at the IMGC. The specimen is brought to high temperatures with a current pulse; during cooling the heat content is dissipated by radiation and by conduction. The differential equation describing this process contains terms related to the heat capacity, the hemispherical total emittance, and the thermal conductivity of the material. If the first two properties are determined using the same specimen during subsecond pulse heating experiments, thermal conductivity may be evaluated by accurate measurements of the round-shaped temperature profiles established on the specimen during cooling. High-speed scanning pyrometry makes possible accurate measurements of temperatures and of temperature derivatives (with respect to space and time), which enables the differential equation describing the power balance at each point of the specimen to be transformed into a linear equation of the unknown thermal conductivity. A large overdetermined system of linear equations is solved by least-squares techniques to obtain thermal conductivity as a function of temperature. The theory underlying the technique is outlined, the experimental apparatus is described, and details of the measurement technique are given.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.     

Thermal conductivity and diffusivity measurements at cryogenic temperatures by double specimen technique

A double specimen technique is used in measuring the thermal conductivity and diffusivity of low thermal conductivity materials. In this technique good thermal contact is maintained between the heat source and sink and two geometrically similar specimens. A thin-copper heater plate is compressed between the two specimens and the temperature difference is measured between the heat source and the temperature controlled heat sink. Thermal conductivity is determined at steady state conditions by the differential method while the diffusivity is determined from transient measurements combined with an analytical solution to the one dimensional solution of the diffusion equation.     

Laser-produced plasma measurement of thermal diffusivity of molten metals

We have shown that a laser-produced plasma plume which is representative in elemental composition of the condensed phase target can be reproducibly generated if the movement of the surface due to evaporation is kept in pace with the thermal diffusion front propagating into the bulk. The resulting mass loss is then strongly controlled by the thermal diffusivity of the target matter, and this relationship has been exploited to measure the thermal diffusivity of metallic alloys. We have developed a novel RF Ievitator-heater as a contamination-free molten metal source to be used as a target for LPP plume generation. In order to determine the mass loss due to LPP excitation, a new high-sensitivity transducer has been constructed for measurement of the resulting impulse imparted on the specimen. The impulse transducer is built onto the specimen holder within the levitation-assisted molten metal source. The LPP method has been fully exercised for measurement of the thermal diffusivity of a molten specimen relative to the value for its room temperature solid. The results for SS304 and SS316 are presented, together with a critique of the results. A numerical modeling of the specimen heating in the molten metal source and the physical basis of the new method are also presented.Paper presented at the Fourth International Workshop on Subsecond Thermophysics, June 27–29, 1995, Köln, Germany.     

点热源热脉冲法测算生物流体的热物性参数

采用微珠状热敏电阻作为点热源和测温元件，在一维点源脉冲传热模型的基础上建立一种同时测量生物流体热扩散系数、导热系数和热容的瞬态方法。运用非线性参数拟合，直接从感温热敏电阻对热脉冲温度响应中同时获取待测的热物性参数。实验中设计了一个高灵敏度的温度测量电路，测试结果表明，本方法测量误差小于4％。此外，还讨论了测量数据的处理和影响测量的因素。     

Service-type creep-fatigue experiments with cruciform specimens and modelling of deformation

Advanced material models for the application to component life prediction require multiaxial experiments. A biaxial testing system for cruciform test pieces has been established in order to provide data for creep, creep-fatigue and thermomechanical fatigue (TMF) experiments. For this purpose a cruciform specimen was developed with the aid of Finite element calculation and the specimen design was optimised for tension and compression load. The testing system is suitable for strain (displacement) and load control mode. A key feature deals with the opportunity to perform thermomechanical experiments. Further, a constitutive material model is introduced which is implemented as a user subroutine for Finite element applications. The constitutive material model of type Chaboche considers both isotropic as well as kinematic hardening and isotropic damage. Identification of material parameters is achieved by a combination of Neural networks and subsequent Nelder–Mead Method.