Characterization of a superplastic aluminium alloy ALNOVI-U through free inflation tests and inverse analysis

Numerical methods are widespread in forming applications since a deeper understanding and a finer calibration of the process can be reached without most of the assumptions used in analytical approaches. In this calibration procedure the characterization of the material behaviour is an important preliminary step that cannot be avoided. Experimental tests can be numerically modelled and material constants can be found by inverse methods making numerical results as close as possible to experimental ones. In this work material parameters of a superplastic aluminium alloy have been found by experimental forming tests and an inverse analysis. Constant pressure free inflation tests were firstly performed to find the optimal range for temperature and strain rate values. Material constants were then calculated, on the basis of these tests, minimizing errors between experimental and numerical data through a gradient based optimization iterative procedure. Constant strain rate experimental tests were finally used to refine material parameters and to gain a better agreement between experiments and numerical simulations.     

Determination of the fracture properties of metallic materials using pre‐cracked small punch tests

In this paper, the use of pre‐cracked small punch test (p‐SPT) miniature specimens to obtain the fracture parameters of a material is presented. The geometry of the specimens used was square of 10 × 10 mm with a thickness of 0.5 mm. An initial crack‐like notch was created in the SPT specimens by means of a laser micro‐cutting technique. In order to obtain the fracture parameters from p‐SPT specimens three different approaches have been considered here. The first approach is based on the crack tip opening displacement concept, the second is based on the measure of the fracture energy using the area under the load–displacement curve for different crack sizes, and the third approach is based on the direct numerical simulation of the p‐SPT specimen and the numerical calculation of the J‐integral. In order to study the crack initiation in these p‐SPT specimens, several interrupted tests and the subsequent scanning electron microscope analysis have been carried out. The results indicate that p‐SPT specimens can be used as an alternative method for determining the fracture properties of a material in those cases where there is not enough material to undertake conventional fracture tests. For these p‐SPT specimens, the multi‐specimen method for the determination of the fracture energy is the most promising approach. The results indicate that this small specimen size allows the value of the material toughness, under low constraint conditions to be obtained.     

Effect of DIC Spatial Resolution,Noise and Interpolation Error on Identification Results with the VFM

The use of experimental tests that involve full‐field measurements to characterize mechanical material properties is becoming more widespread within the engineering community. In particular digital image correlation (DIC) on white light speckles is one of the most used tools, thanks to the relatively low cost of the equipment and the availability of dedicated software. Nonetheless the impact of measurement errors on the identified parameters is still not completely understood. To this purpose, in this paper, a simulator able to numerically simulate an experimental test, which involves DIC is presented. The chosen test is the Unnotched Iosipescu test used to identify the orthotropic elastic parameters of composites. Synthetic images are generated and then analysed by DIC. Eventually the obtained strain maps are used to identify the elastic parameters with the Virtual Fields Method (VFM). The numerical errors propagating through the simulation procedure are carefully characterized. Besides, the simulator is used to compare the performances of DIC and the grid method in the identification process with the VFM. Finally, the influence of DIC settings on the identification error is studied as a function of the camera digital noise level, in order to find the best testing configuration.     

Numerical modeling and simulation of wheel radial fatigue tests

A computational methodology is proposed for fatigue damage assessment of metallic automotive components and its application is presented with numerical simulations of wheel radial fatigue tests. The technique is based on the local strain approach in conjunction with linear elastic FE stress analyses. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Critical plane damage parameters are used in the characterization of fatigue damage under multiaxial loading conditions. All computational modules are implemented into a software tool and used in the simulation of radial fatigue tests of a disk-type truck wheel. In numerical models, the wheel rotation is included with a nonproportional cyclic loading history, and dynamic effects due to wheel–tire interaction are neglected. The fatigue lives and potential crack locations are predicted using effective strain, Smith–Watson–Topper and Fatemi–Socie parameters using computed stress–strain histories. Three-different test conditions are simulated, and both number of test cycles and crack initiation sites are estimated. Comparisons with the actual tests proved the applicability of the proposed approach.     

Application of a split-Hopkinson tension bar in a mutual assessment of experimental tests and numerical predictions

This paper shows how experimental test results from a split-Hopkinson tension bar (SHTB) and numerical simulations of the test set-up can be used for mutual verification. Firstly, a SHTB where the tension stress wave is generated by pre-stretching a part of the incident bar is briefly presented. This SHTB is used to carry out tensile tests of four aluminium alloys at high rates of strain, while tests at low to medium strain rates were performed in a servo-hydraulic tensile test machine. Using the test results, the parameters of an anisotropic thermoelastic-thermoviscoplastic constitutive relation and a one-parameter fracture criterion are identified for the materials at hand. Subsequently, the material model is used in explicit finite element analyses of the SHTB tests, including the entire experimental set-up and the stress wave propagation during the test. The numerical predictions were found to represent the observed behaviour in the experimental tests fairly well.     

Virtual Fields Method on Planar Tension Tests for Hyperelastic Materials Characterisation

Abstract: New methods are emerging in the material characterisation field with the aim of exploiting innovative full‐field strain measurement techniques. Besides experimental issues, also numerical procedures for inverse problems should adapt to a new philosophy: the large amount of data referred to local strains should be used in an appropriate way to obtain as much benefits as possible. In this context, an experimental and numerical procedure for the characterisation of hyperelastic materials is proposed. Planar tension tests have been performed on flat rubber specimens of different geometries. Strain maps obtained by means of a 2D Digital Image Correlation system are used to implement the virtual fields method, to estimate material dependent parameters of two of the most known hyperelastic constitutive laws: Ogden and 2nd order Mooney‐Rivlin models. Numerical results and comparisons with experimental data are shown, analysing also aspects concerning implementation of the numerical procedures and computational efficiency of the algorithms.     

Mechanical behaviour and 3D stress analysis of multi-layered wooden beams made with welded-through wood dowels

This paper presents experimental and numerical investigations on multi-layered timber beams using welded-through wood dowels in place of traditional poly(vinyl acetate) (PVAc)-adhesives (or metallic nails). Four-layer beams were constructed with varying numbers of dowels, in each, and then loaded using four-points bending tests to evaluate the mechanical performance of these beams. The practical difficulties encountered in constructing deeper multi-layer beams are discussed and possible solutions which have been employed for the purpose of this work, and proved successful are presented. In order to investigate thoroughly the full potential of multi-layered beams with a very limited number of experimental studies, a 3D FE model has been presented, validated against experimental results and then used to study some influential parameters. The results showed that a reasonable bending stiffness of multi-layered beams is achievable with a good combination of material and geometric parameters.     

A non-linear stochastic approach of ligaments and tendons fractional-order hereditariness

In this study the non-linear hereditariness of knee tendons and ligaments is framed in the context of stochastic mechanics. Without losing the possibility of generalization, this work was focused on knee Anterior Cruciate Ligament (ACL) and the tendons used in its surgical reconstruction. The proposed constitutive equations of fibrous tissues involves three material parameters for the creep tests and three material parameters for relaxation tests. One-to-one relations among material parameters estimated in creep and relaxations were established and reported in the paper. Data scattering, observed with a novel experimental protocol used to characterize the mechanics of the tissue, was modelled as the outcome of the random mechanical parameters. The numerical example proposed in the paper shows that for an assigned probability density function of the material random parameters, the parameters of the probability density function (pdf) may be obtained by a statistical analysis of the experimental data.     

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.     

Monitoring of non-homogeneous strains in composites with embedded wavelength multiplexed fiber Bragg gratings: A methodological study

For the detection of problems like fastening failures and delamination in composites, the employment of embedded fiber Bragg grating (FBG) sensors is considered an effective tool to measure non-homogeneous internal strains near damage or interfaces of dissimilar materials which in turn can help identify the severity of fracture. In this work wavelength multiplexed FBGs are used to measure strains during gradual adhesive fastening failure in a single lap joint and delamination in a uniaxial composite, during monotonic and fatigue loads. It is shown that such measurements can be effectively used to determine the stresses near the joint and bridging tractions in delamination. The particular method can provide a significant tool in experimental mechanics and fatigue of composites as well as composite assemblies. Experimental measurements are in very good agreement with the numerical analysis concurrently used for the verification of the experimental procedure’s feedback.     

Parameter identification of hardening laws for bulk metal forming using experimental and numerical approach

The simulative prediction of material behaviour in forming processes necessitates a precise determination of the material parameters. The present work focusses on the modelling of the isostatic part of the flow stress using a flow curve with an analytical suppression of the influence of friction and an adequate analytical law. The experimental data are obtained from isothermal upsetting tests with various upsetting ratios. The different ratios are based on a variation of the height of the sample, remaining the diameter constant. For the proposed flow stress law five parameters are identified. In order to decrease the number of function evaluations, a new reduction model method based on both analytical and sequential quadratic programming (SQP) algorithms is developed and applied to identify flow stress law parameters. A comparison with traditional SQP algorithm is also done. A 3D finite element model is built in order to simulate a side pressing test and an experimental validation is done. As numerical results fit very well experimental data, the proposed model achieves a precise prediction of the flow behaviour. The identification of the other parts of the model (i.e. dependencies on strain-rate and temperature) are conducted in further works.     

Damage Model and Progressive Failure Analyses for Filament Wound Composite Laminates

Recent improvements in manufacturing processes and materials properties associated with excellent mechanical characteristics and low weight have made composite materials very attractive for application on civil aircraft structures. However, even new designs are still very conservative, because the composite failure phenomenon is very complex. Several failure criteria and theories have been developed to describe the damage process and how it evolves, but the solution of the problem is still open. Moreover, modern filament winding techniques have been used to produce a wide variety of structural shapes not only cylindrical parts, but also “flat” laminates. Therefore, this work presents the development of a damage model and its application to simulate the progressive failure of flat composite laminates made using a filament winding process. The damage model was implemented as a UMAT (User Material Subroutine), in ABAQUS^TM Finite Element (FE) framework. Progressive failure analyses were carried out using FE simulation in order to simulate the failure of flat filament wound composite structures under different loading conditions. In addition, experimental tests were performed in order to identify parameters related to the material model, as well as to evaluate both the potential and the limitations of the model. The difference between numerical and the average experimental results in a four point bending set-up is only 1.6 % at maximum load amplitude. Another important issue is that the model parameters are not so complicated to be identified. This characteristic makes this model very attractive to be applied in an industrial environment.     

Thermo-mechanical fatigue resistance characterization and materials ranking from heat-flux-controlled tests. Application to cast-irons for automotive exhaust part

In a context where the mass, the cost and the mechanical strength of materials must be jointly optimized, it is necessary to have experimental data quickly available and sufficiently robust to make efficient conception choices. For thermomechanical fatigue, standard tests usually allow comparing material for the same temperature and strain ranges although differences in thermal properties such as conductivity or thermal expansion could make significant deviations when the same thermal flux is applied particularly for structure with forced heat flux operating regimes. A new protocol is then proposed in order to compare the specific resistances of metallic materials against thermomechanical fatigue. It can easily rank materials according to their lifetime under thermomechanical loadings where strain range and temperature amplitude are determined by the heat flux applied on an industrial part. The method is based on a complete numerical analysis to determine experimental loading conditions as a temporal evolution of temperature and mechanical strain representative of thermomechanical loading observed in TMF critical areas for the part. TMF tests on hollow specimens are carried out to rank the materials: temperature and strain amplitude are different for each alloys whereas heat flux is identical. A materials ranking list based on TMF resistance is then determined according to their lifetimes under “heat-flux-controlled” tests. The method is tested for exhaust parts and demonstrates the superiority of some cast irons over others, whereas the intrinsic isotherm mechanical properties suggested an alternative classification. The obtained ranking is confirmed by experimental tests on industrial structures.     

Continuous fatigue damage prediction of a rubber fibre composite structure using multiaxial energy‐based approach

This paper details an advanced method of continuous fatigue damage prediction of rubber fibre composite structures. A novel multiaxial energy‐based approach incorporating a mean stress correction is presented and also used to predict the fatigue life of a commercial vehicle air spring. The variations of elastic strain and complementary energies are joined to form the energy damage parameter. Material parameter α is introduced to adapt for any observed mean stress effect as well as being able to reproduce the well‐known Smith‐Watson‐Topper criterion. Since integration to calculate the energies is simplified, the approach can be employed regardless of the complexity of the thermo‐mechanical load history. Several numerical simulations and experimental tests were performed in order to obtain the required stress‐strain tensors and the corresponding fatigue lives, respectively. In simulations, the rubber material of the air spring was simulated as nonlinear elastic. The mean stress parameter α , which controls the influence of the mean stress on fatigue life, was adjusted with respect to those energy life curves obtained experimentally. The predicted fatigue life and the location of failure are in very good agreement with experimental observations.     

Hyperelastic Behaviour Identification by a Forward Problem Resolution: Application to a Tear Test of a Silicone-Rubber

Abstract:  The mechanical behaviour of synthetic rubbers shows very high deformability, compressibility, time-dependent effect and strain softening. The present study is devoted to the analysis of local mechanical behaviour of silica-filled silicone rubber. New testing and identification are proposed in this paper by using standardised tear test, kinematic field measurements and a numerical inverse problem resolution to investigate localisation strain phenomena. The experimental procedure described hereafter, is based on strain field measurements using digital image processing. In-plane kinematic measurements by the digital image correlation are suitable to analyse non-homogeneous mechanical tests performed especially on thin sheets: indeed, rubber-like materials are characterised by a very high deformability and a non-linear behaviour leading to important gradients of deformation. The identification procedure is conducted in two steps. First, parameters of the viscosity and stress softening (Mullins effect) are evaluated analytically by using axial and biaxial tensile tests. Then, hyperelastic parameters are identified by an inverse resolution based on standardised tear tests. The mechanical model is implemented into the finite element code Zebulon (Transvalor/ENSMP). The numerical model is built up by using informations on geometry and boundary conditions extracted from image sequence that were acquired during the test. Usage of different functions evaluating the distance between computed and experimental quantities (cost functions) in a minimisation process is discussed.     

Parameter determination and experimental verification of Bergström–Boyce hysteresis model for rubber compounds reinforced by carbon black blends

This research work is devoted to the modeling of the hyper-viscoelastic behavior of rubber compounds using Bergström–Boyce hysteresis model. Two series of rubber compounds reinforced by different carbon black types and amounts were prepared. In the first series single type filler was used while in the second series the blend of two carbon black types was employed. The mechanical behaviors of these samples were studied using a hyper-viscoelastic model which was based on the combination of Yeoh hyperelastic model and Bergström–Boyce hysteresis model implemented in the Abaqus software. A hybrid numerical/experimental technique developed in our previous works was employed to determine the parameters of the Bergström–Boyce model for the mentioned samples. In this technique uniaxial tests were carried out on three rubber strips specimens and the data of force vs. extension were recorded. These data were used in three finite element models to calibrate the material parameters for the aforementioned model and the relationship between particle size and structural measure of the carbon black with parameters of the Bergström–Boyce model were completely discussed.     

Indentation and imprint mapping for the identification of interface properties in film-substrate systems

Indentation tests are frequently employed at present for the identification of material parameters at different scales. An innovative inverse analysis technique, recently proposed by the Authors, combines the traditional indentation test with the mapping of the residual deformations (imprint), thus providing experimental data apt to be used to identify material parameters in film-substrate systems. In this paper, such methodology is enhanced to permit the identification of the fracture properties of the interface between a coating and its substrate once the bulk material parameters are known. In order to make the inverse problem well posed, a further set of experimental data, namely the horizontal displacement field measured on the film external surface, is considered as available experimental information. The sought material parameters are recovered through recursive calculations of the mechanical response of the film-substrate system, performed by a finite strain numerical simulation. The coating and a significant portion of the underlying bulk material are incorporated in the finite element models built up to this purpose, while delamination is accounted for through cohesive elements. The inverse analysis procedure rests on a batch, deterministic approach and conventional optimization algorithms are employed for the minimization of a suitably defined discrepancy norm. Extensive numerical computations have been performed in order to test the performance of the proposed methodology in terms of result accuracy and computational effort.