Determination of plastic yield stress from spherical indentation slope curve

The indentation slope curve from a spherical indentation on elastic-plastic materials is examined. By comparing it with that of an linear elastic material of the same elastic properties, we found that the start point of plastic yielding for an elastic-plastic material can be easily located from the indentation slope curve. Based on this analysis, a simple but effective method is proposed to measure the plastic yield stress of very small samples from a spherical nano-indentation slope curve.

Theoretical extension of elastic-perfectly plastic deformation length in roll forming of a channel section

In this paper, the Young’s modulus and the yield strength of the strip are considered in order to modify the deformation length analysis proposed by Bhattacharyya et al. New analytical equations are developed assuming an elastic-perfectly plastic material behaviour and the deformation length analysed for the simple case of roll forming a U-channel; the analytical results are verified by comparison with experimental data found in the literature. The proposed elastic-plastic deformation length is shorter than Bhattacharyya’s which is rigid-perfectly plastic. It is observed that the influence of elastic properties on the deformation length is not as significant as the plastic properties; however, the authors believe that the elastic effects become more important under conditions where a major area of the strip is under elastic deformation such as when the flange length is long.

Effect of roller leveling on the bending behaviour of aged steel strip

The common grades of steel used in roll forming are: hot rolled carbon steel, high strength low alloy and recovery annealed cold rolled sheet. These steels are prone to ageing and are often skin passed and/or roller leveled to eliminate ageing as it can lead to problems in forming. In roll forming, shape defects such as bow, twist and camber are considered to be related to very small plastic strains in the longitudinal direction and hence knowledge of the material properties in the elastic plastic transition range is necessary if the process is to be modelled accurately. Previous studies with aluminium have indicated that skin pass rolling can lead to residual stresses in the strip. In this work, the study was extended to aged carbon steel and to the effect of roller leveling on both aged material and strip that had been given a light cold rolling to simulate a skin pass treatment. The results suggest that roller leveling reduced the magnitude of residual stresses resulting from skin pass rolling.

The significant differences observed between tensile and bending test results, at and near, the elastic plastic transition reinforces the need to consider bending properties when assessing the effect of prior processing on strip for roll forming.

Effect of tensile pre-strain on bending and unloading of automotive steels

In recent years, advanced high strength steels (AHSS) have been used in a wide range of automotive applications; they may have property variations through the thickness and the properties may also be dependent of prior processing including pre-straining. In order to model forming processes precisely using, for example, finite element analysis, it is important that material input data should adequately reflect these effects. It is known that shape defects in roll forming are related to small strains in material that has undergone prior deformation in a different strain path. Much research has already been performed on the change in the Young’s Modulus once a steel sheet has been plastically deformed,however many of these tests have only been conducted using tensile testing, and therefore may not take into account differences in compressive and tensile unloading. This research investigates the effect of tensile pre-straining on bending behaviour for various types of material;in bending, one half of the sheet will load and unload in compression and hence experience deformation under a reversed stress. Four different materials were pre-strained in tension with 1%, 3%, 7%, 11% and 25% elongation. Using a free bending test, moment curvature diagrams were obtained for bending and unloading. The results showed that the characteristics of the moment curvature diagram depended on the degree of pre-straining; more highly strained samples showed an earlier elastic-plastic transformation and a decreased Young's Modulus during unloading. This was compared to previous literature results using only tensile tests. Our results could influence the modeling of springback in low tension sheet operations, such as roll forming.

Constitutive modelling of high strength titanium alloy Ti-6Al-4 V for sheet forming applications at room temperature

To enable the design and optimisation of forming processes at room temperature the material behaviour of Ti-6Al-4 V needs to be accurately represented in numerical analysis and this requires an advanced material model. In particular, an accurate representation of the shape and size of the yield locus as well as its evolution during forming is important. In this study a rigorous set of experiments on the quasi-static deformation behaviour of a Ti-6Al-4 V alloy sheet sample at room temperature was conducted for various loading conditions and a constitutive material model developed. To quantify the anisotropy and asymmetry properties, tensile and compression tests were carried out for different specimen orientations. To examine the Bauschinger effect and the transient hardening behaviour in - plane tensile - compression and compression - tensile tests were performed. Balanced biaxial and plane strain tension tests were conducted to construct and validate the yield surface of the Ti-6Al-4 V alloy sheet sample at room temperature. A recently proposed anisotropic elastic-plastic constitutive material model, so-called HAH, was employed to describe the behaviour, in particular for load reversals. The HAH yield surface is composed of a stable component, which includes plastic anisotropy and is distorted by a fluctuating component. The key of the formulation is the use of a suitable yield function that reproduces the experimental observations well for the stable component. Meanwhile, the rapid evolution of the material structure must be captured at the macro - scale level by the fluctuating component embedded in the HAH model. Compared to conventional hardening equations, the proposed model leads to higher accuracy in predicting the Bauschinger effect and the transient hardening behaviour for the Ti-6Al-4 V sheet sample tested at room temperature.

Prediction of failure in bending of an aluminium sheet alloy

This work is dedicated to numerical prediction of the bending of thin aluminium alloy sheets, with a focus on the material parameter identification and the prediction of rupture with or without pre-strains in tension prior to bending. The experimental database consists of i) mechanical tests at room temperature, such as tension and simple shear, performed at several orientations to the rolling direction and biaxial tension ii) air bending tests of rectangular samples after (or not) pre-straining in tension. The mechanical model is composed of the Yld2004-18p anisotropic yield criterion (Barlat et al. [3]) associated with a mixed hardening rule. The material parameters (altogether 21) are optimized with an inverse approach, in order to minimize the gap between experimental data and model predictions. Then, the Hosford-Coulomb rupture criterion is used in an uncoupled way, and the parameters are determined from tensile tests, both uniaxial and biaxial, with data up to rupture. In a second step, numerical simulations of the bending tests are performed, either on material in its original state or after pre-straining in tension, with pre-strain magnitudes increasing from 0.19 up to 0.3. The comparisons are performed on different outputs: load evolution, strain field and prediction of the rupture. A very good correlation is obtained over all the tests, in the identification step as well as in the validation one. Moreover, the fracture criterion proves to be successful whatever the amount of pre-strain may be. A convincing representation of the mechanical behavior at room temperature for an aluminium alloy is thus obtained.

Development of a laboratory-based transmission diffraction technique for in situ deformation studies of Mg alloys

A laboratory-based transmission X-ray diffraction technique was developed to measure elastic lattice strains parallel to the loading direction during in situ tensile deformation. High-quality transmission X-ray diffraction data were acquired in a time frame suitable for in situ loading experiments by application of a polycapillary X-ray optic with a conventional laboratory Cu X-ray source. Based on the measurement of two standard reference materials [lanthanum hexaboride (NIST SRM 660b) and silicon (NIST SRM 640c)], precise instrumental alignment and calibration of the transmission diffraction geometry were realized. These results were also confirmed by the equivalent data acquired using the standard Bragg-Brentano measurement geometry. An empirical Caglioti function was employed to describe the instrumental broadening, while an axis of rotation correction was used to measure and correct the specimen displacement from the centre of the goniometer axis. For precise Bragg peak position and hkil intensity information, a line profile fitting methodology was implemented, with Pawley refinement used to measure the sample reference lattice spacings (d o (hkil)). It is shown that the relatively large X-ray probe size available (7 × 714mm) provides a relatively straightforward approach for improving the grain statistics for the study of metal alloys, where grain sizes in excess of 114μm can become problematic for synchrotron-based measurements. This new laboratory-based capability was applied to study the lattice strain evolution during the elastic-plastic transition in extruded and rolled magnesium alloys. A strain resolution of 2 × 10-4 at relatively low 2θ angles (20-65° 2θ) was achieved for the in situ tensile deformation studies. In situ measurement of the elastic lattice strain accommodation with applied stress in the magnesium alloys indicated the activation of dislocation slip and twin deformation mechanisms. Furthermore, measurement of the relative change in the intensity of 0002 and 10 3 was used to quantify {10 2} 011 tensile twin onset and growth with applied load.

Conductivity, NMR and crystallographic study of N,N,N,N-tetramethylammonium dicyanamide plastic crystal phases : an archetypal ambient temperature plastic electrolyte material

N,N,N,N-Tetramethylammonium dicyanamide (Me₄NDCA) has been examined via differential scanning calorimetry (DSC), thermogravimetric analysis, conductivity, single crystal X-ray diffraction and ¹H nuclear magnetic resonance (NMR) analyses, and was found to be highly conductive in the solid state (σ =10−3 S cm⁻² at 420 K) and to also exhibit unusual plastic crystal behaviour. To investigate the correlation between such behaviour and the occurrence of molecular rotations in the crystal, ¹H NMR second moment measurements are compared with calculated values predicted from the crystal structure. While DSC analysis indicates a number of solid–solid transitions at ambient temperatures, subsequent ¹H NMR analysis of the Me₄N⁺ cation shows that a variety of rotational motions become active at low (<240 K) temperatures, and that such transitions in rotational states occur over a range of temperatures rather than in a sharp transition. Conductivity analysis reveals that between 320 K and 420 K the conductivity increases by more than six orders of magnitude in the solid state, in line with the transition of the Me₄N⁺ cation to a diffusive state, and that other phase transitions observed in this temperature range have no marked effect on the conductivity. Conduction in this solid state is therefore envisaged to involve a vacancy-diffusion model, involving Me₄N⁺ cation vacancies.

Plastic water the social and material life of bottled water

How did branded bottles of water insinuate themselves into our daily lives? Why did water become an economic good—no longer a common resource but a commercial product, in industry parlance a “fast moving consumer good,” or FMCG? Plastic Water examines the processes behind this transformation. It goes beyond the usual political and environmental critiques of bottled water to investigate its multiplicity, examining a bottle of water’s simultaneous existence as, among other things, a product, personal health resource, object of boycotts, and part of accumulating waste matter. Throughout, the book focuses on the ontological dimensions of drinking bottled water—the ways in which this habit enacts new relations and meanings that may interfere with other drinking water practices.

Effect of elastic modulus and poisson's ratio on guided wave dispersion using transversely isotropic material modelling

Timber poles are commonly used for telecommunication and power distribution networks, wharves or jetties, piling or as a substructure of short span bridges. Most of the available techniques currently used for non-destructive testing (NDT) of timber structures are based on one-dimensional wave theory. If it is essential to detect small sized damage, it becomes necessary to consider guided wave (GW) propagation as the behaviour of different propagating modes cannot be represented by one-dimensional approximations. However, due to the orthotropic material properties of timber, the modelling of guided waves can be complex. No analytical solution can be found for plotting dispersion curves for orthotropic thick cylindrical waveguides even though very few literatures can be found on the theory of GW for anisotropic cylindrical waveguide. In addition, purely numerical approaches are available for solving these curves. In this paper, dispersion curves for orthotropic cylinders are computed using the scaled boundary finite element method (SBFEM) and compared with an isotropic material model to indicate the importance of considering timber as an anisotropic material. Moreover, some simplification is made on orthotropic behaviour of timber to make it transversely isotropic due to the fact that, analytical approaches for transversely isotropic cylinder are widely available in the literature. Also, the applicability of considering timber as a transversely isotropic material is discussed. As an orthotropic material, most material testing results of timber found in the literature include 9 elastic constants (three elastic moduli and six Poisson's ratios), hence it is essential to select the appropriate material properties for transversely isotropic material which includes only 5 elastic constants. Therefore, comparison between orthotropic and transversely isotropic material model is also presented in this article to reveal the effect of elastic moduli and Poisson's ratios on dispersion curves. Based on this study, some suggestions are proposed on selecting the parameters from an orthotropic model to transversely isotropic condition.

Evolution of elastic modulus in roll forming

Roll forming is a continuous process in which a flat strip is incrementally bent to a desired profile. This process is increasingly used in automotive industry to form High Strength Steel (HSS) and Advanced High Strength Steel (AHSS) for structural components. Because of the large variety of applications of roll forming in the industry, Finite Element Analysis (FEA) is increasingly employed for roll forming process design. Formability and springback are two major concerns in the roll forming AHSS materials. Previous studies have shown that the elastic modulus (Young’s modulus) of AHSS materials can change when the material undergoes plastic deformation and the main goal of this study is to investigate the effect of a change in elastic modulus during forming on springback in roll forming. FEA has been applied for the roll forming simulation of a V-section using material data determined by experimental loading-unloading tests performed on mild, XF400, and DP780 steel. The results show that the reduction of the elastic modulus with pre-strain significantly influences springback in the roll forming of high strength steel while its effect is less when a softer steel is formed.

Numerical models of plastic zones and associated deformations for elliptical inclusions in remote elastic loading-unloading with different R-ratios

Plastic zones and associated deformations ahead of a fatigue crack are well established nowadays. In-depth plane strain elasto-plastic finite element analysis is conducted in this investigation to understand the nature of cyclic plastic deformation and damage around soft and hard elliptical inclusions. Similar to fatigue crack tip, cyclic/reverse plastic zone and monotonic plastic zone are visible for soft elliptical inclusion. In the cyclic plastic zone, low cycle fatigue is the dominant cyclic deformation mode during symmetric load cycling, while ratcheting is dominant during asymmetric load cycling. The size of cyclic plastic zone depends upon the amplitude of remote stress while, the size of monotonic plastic zone depends upon the maximum remote stress. The size of monotonic plastic zone is equal to cyclic plastic zone during symmetric load cycling. The shape and size of plastic zones also depend upon the orientation of the soft inclusion. Cyclic plastic damage progression in the cyclic plastic zone for soft (MnS) inclusion is significant, while no cyclic plastic zone is visible for hard inclusion (Al2O3).

Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour

In the empirical methods for reinforcement design of underground excavations, an even distribution of rock bolts is generally recommended. This work proves that this design is not necessarily optimal and shows how the state-of-the-art reinforcement design could be improved through topology optimisation techniques. The Bidirectional Evolutionary Structural Optimisation (BESO) method has been extended to consider nonlinear material behaviour. An elastic perfectly-plastic Mohr-Coulomb model is utilised for both original rock and reinforced rock. External work along the tunnel wall is considered as the objective function. Various in situ stress conditions with different horizontal stress ratios and different geostatic stress magnitudes are investigated through several examples. The outcomes show that the proposed approach is capable of improving tunnel reinforcement design. Also, significant difference in optimal reinforcement distribution for the cases of linear and nonlinear analysis results proves the importance of the influence of realistic nonlinear material properties on the final outcome.

The mechanical characterization of low work hardening, high strength steel

One of the major challenges in assessing the mechanical properties of recovery annealed steel is the strain localization that occurs almost immediately on the formation of the first Lüders band, such that no or limited propagation of the Lüders band occurs along the tensile coupon. The stress raiser associated with the geometry of the standard tensile coupon means that this plastic deformation is often completely outside the standard extensometers on the coupon. Hence, no strain is measured during the test. While this is not important for assessing the tensile strength of the steel, it does mean that the strain related properties, such as the elastic limit of the steel, cannot be measured using standard testing techniques.This work addresses this issue by examining three techniques for ensuring that the strain occurs inside the extensometer. It is shown that the best technique is the extended extensometer, where the gauge length covers slightly more than the tensile coupon parallel length. While this leads to some variation in the width of the material being measured, compensation can be be made by adjusting the strain to correct the Young's Modulus.This technique has direct implications not just for recovery annealed steels, but for other high strength, low work hardening materials such as ultrafine ferrite. A particular requirement of these high strength steels in structural applications is a high elastic limit; hence, measurement of the strain related properties for these high strength materials must be considered vital in their mechanical assessment.