Compressive Stress-strain Data Research Articles

Experimental Characterisation and Finite Element Modelling of Polyamide-12 Fabricated via Multi Jet Fusion.

The HP Multi Jet Fusion (MJF) technology is a relatively recent addition to powder bed fusion additive manufacturing (AM) techniques. It differentiates itself from selective laser sintering (SLS) technology through the use of fusing and detailing agents to control part geometry, and the use of a planar infrared radiation (IR) source that sweeps over the powder bed to initiate the sintering process. Depending on the printing methodology, AM processes can introduce mechanical property anisotropy that is dependent on print orientation. In the case of MJF-fabricated parts, there is a general disagreement over the influence of print orientation on tensile mechanical properties in the literature. In this work, MJF-fabricated PA12 (AM PA12) is printed at various orientations and characterised in terms of tensile and compressive mechanical properties. The orientations have been selected to take into account the alignment of the IR source sweep direction to the test load. We observe that orientating parts towards the vertical direction for printing tends to favour enhanced tensile mechanical properties. The anisotropy in mechanical properties is attributed to more complete polymer powder fusion as a result of the increased number of IR source sweeps when parts are orientated towards the vertical direction. Both tensile and compressive stress-strain data were used as experimental data input for calibrating the Elastic-Plastic with combined hardening (EPC) material model in the commercial finite element analysis (FEA) package-Abaqus. We demonstrate that the EPC material is a suitable material model for the FEA of AM PA12.

High strain rate compressive behaviour of 6000-series aluminium alloy sheet under SHPB impact loading

High velocity forming technologies are widely used in manufacturing industries to improve the formability of the aluminum alloy sheets. In order to better control the high velocity forming technologies through numerical simulation, the dynamic compression properties of the thin 6000-series aluminum alloy sheet were investigated by SHPB experiments. The influence of strain rate on the mechanical properties is analyzed in detail. Results show the elastic modulus is independent of the strain rate. However, under high strain rate condition, the yield stress, ultimate compression strength and ductility enhance with the increased high strain rate. So this 6000-series aluminum alloy sheet has significant strain rate sensitivity. As a reference, the quasi-static uniaxial tension test is also carried out and the uniaxial compressive stress-strain data in the literature is also listed. However, it is found the quasi-static uniaxial tensile yield stress is larger than the uniaxial compressive yield stress, and the quasi-static uniaxial compressive yield stress is lower than that under dynamic compressive condition. Results prove the aluminum alloy has obvious tension-compression anisotropy. For the high velocity forming technologies that take stretching as the main deformation mode, the dynamic tensile behaviour, instead of the dynamic compressive behaviour, should be used for accurate simulation.

A data-driven multi-scale constitutive model of concrete material based on polynomial chaos expansion and stochastic damage model

Nonlinearity and randomness are two intrinsic characteristics of the mechanical behavior of concrete material. The structural response under large excitation can barely be predicted without considering these two characteristics. Brilliant works have been done for decades in the material science and computational stochastic mechanics. However, the existed numerical methods are usually parameter dependent and the key mechanical properties of concrete material are determined by empirical recognition. Therefore, in this paper, a data-driven multi-scale constitutive model is proposed for representing the mechanical behavior of concrete material based on the polynomial chaos expansion and stochastic damage model. Several groups of compressive stress–strain data of concrete material are applied to train the proposed model. By cross validation of the prediction and the concrete stress–strain experimental data, the proposed model is firstly verified to have a robust performance to gain accurate prediction results. Afterwards, the proposed method is compared with a neural network method, the results shows that the proposed method is more robust and accurate than the neural network method.

Characterisation of Compressive Behaviour of Low-Carbon and Third Generation Advanced High Strength Steel Sheets with Freely Movable Anti-buckling Bars

Measuring the compressive behaviour of sheet materials is an important process for understanding the material behaviour and numerical simulation of metal forming. The application of side force on both surfaces of a specimen in the thickness direction is an effective way to prevent buckling when conducting compressive tests. However, the side effects of side forces (such as the biaxial stress state and non-uniform deformation) make it difficult to interpret the measured data and derive the intrinsic compressive behaviour. It is even more difficult for materials with tension–compression asymmetry such as steels that undergo transformation-induced plasticity. In this study, a novel design for a sheet compression tester was developed with freely movable anti-buckling bars on both sides of the specimen to prevent buckling during in-plane compressive loading. Tensile and compressive tests under side force were conducted for low-carbon steel using the digital image correlation method. The raw tensile and compressive stress–strain data of the low-carbon steel showed apparent flow stress asymmetry of tension and compression, originating from the biaxial and thickness effects. A finite element method-based data correction procedure was suggested and validated for the low-carbon steel. The third generation advanced high strength steels showed intrinsic tension–compression asymmetry at room temperature whereas the asymmetry was significantly reduced at 175 °C.

Multi-sensor optimal deployment based efficient and synchronous data acquisition in large three-dimensional physical similarity simulation

PurposeThis paper aims to propose a deployment optimization and efficient synchronous acquisition method for compressive stress sensors used by stress distribution law research based on the genetic algorithm and numerical simulations. The authors established a new method of collecting the mining compressive stress-strain distribution data to address the problem of the number of sensors and to optimize the sensor locations in physical similarity simulations to improve the efficiency and accuracy of data collection.Design/methodology/approachFirst, numerical simulations were used to obtain the compressive stress distribution curve under specific mining conditions. Second, by comparing the mean square error between a fitted curve and simulation data for different numbers of sensors, a genetic algorithm was used to optimize the three-dimensional (3D) spatial deployment of sensors. Third, the authors designed an efficient synchronous acquisition module to allow distributed sensors to achieve synchronous and efficient acquisition of hundreds of data points through a built-in on-board database and a synchronous sampling communication structure.FindingsThe sensor deployment scheme was established through the genetic algorithm, A synchronous and selective data acquisition method was established for reduced the amount of sensor data required under synchronous acquisition and improved the system acquisition efficiency. The authors obtained a 3D compressive stress distribution when the advancement was 200 m on a large-scale 3D physical similarity simulation platform.Originality/valueThe proposed method provides a new optimization method for sensor deployment in physical similarity simulations, which improves the efficiency and accuracy of system data acquisition, providing accurate acquisition data for experimental data analysis.

Friction stir welding of AA2024-T3: development of numerical simulation considering thermal history and heat generation

This paper proposes a finite element model implemented in ANSYS using Lagrangian formulation to assess heat generation and friction dynamics of a friction stir welding process on AA2024-T3 aluminum plates. For that aim, the model is enriched by estimating a temperature-dependent friction coefficient using theoretical relationships, and by considering a temperature-dependent multilinear isotropic hardening equation as a plasticity model representing the material. Both quantitative determinations are confirmed through experimental data collected on the real material. Finally, the contact conditions are modeled using the modified Coulomb criterion. The results of the model are in agreement with actual results observed on experimental applications. The study proves that the rotational speed of the tool is the most determinant factor in the results. As it rises, the friction-generated heat flow is higher. This study shows that the compressive stress-strain data in strain rate of 10s−1 is a good approximation of the plasticity behavior of aluminum alloy during the friction stir welding.

Investigating the Feasibility of a Cushion Selection Method on Polyethylene Based on a Predictive Model

Cushion materials are very popular and widely used in various applications. Cellular solid has been used for cushioning for many years due to its low weight and high energy absorption capacity. Cushioning selection is the process of selecting a cushioning material to sufficiently cushion an object. There are a few cushion selection methods available in literature. The objective of this report is to investigate the feasibility of a cushion selection method based on predicting the impact absorption capacity from static compressive stress-strain data. This is achieved by comparing the predicted dimensionless deceleration (G) and the measured G. Polyethylene (foam) samples were used to conduct the compression test and drop test. For polyethylene, the predicted G shown higher accuracy at low drop height and became lower accuracy with increasing drop height. A dynamic factor C was introduced to account for the difference. From this report, researchers may explore the feasibility of this cushion selection method on polyethylene or even conduct experiments on other cellular solid specimens in the future.

Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor (X) was introduced, the theoretical model could fit the tensile stress-strain data of mono- and bi-modal foam matrix well (Adj. R-Square = 0.9989, 0.9983). Parameters related to the polymer network, namely, average molecular weight (Mc) and volume fraction (ϕ) of chain segments between adjacent cross-linking points (network strands), were calculated by probabilistic method from the number-average molecular weight (Mn), vinyl content (wVi) of the primary polysiloxanes and percent conversion (q) of vinyl groups. The primary and infinite strain amplification factors (X0, X∞) and decay exponent (z), introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams’, we introduced another item, strain hysteresis item (H, related with the foam porosity and cell structure), into the statistical model as well. With the same above values of Mc, ϕ, X0 and X∞, the model could also fit the compressive stress-strain data of mono- and bi-modal foams well (Adj. R-Square = 0.9948, 0.9985). Interestingly, the strain hysteresis items of the mono- and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.

Compressive mechanics of warp-knitted spacer fabrics. Part II: a dynamic model

This part presents a dynamic model for predicting the impact compressive responses of warp-knitted spacer fabrics under various loading conditions using quasi-static compressive stress–strain data. The model was established based on a nonlinear mass-spring-damper system by considering spacer yarns as nonlinear springs with damping effect and representation of their stiffness by the constitutive model developed in Part I. Based on the dynamic model, the impact compressive responses of a typical warp-knitted spacer fabric was parametrically studied in terms of damping ratio, initial velocity, striker mass and contact area. The study indicates that damping can reduce the peak acceleration and peak displacement regardless of loading conditions, and the increase of the initial velocity can enhance the damping effect. Increasing initial velocity or striker mass while keeping the counterpart constant can increase the peak acceleration and peak displacement. However, at a constant kinetic energy, either increasing striker mass or decreasing initial velocity can reduce the peak acceleration, but the peak displacement keeps constant. The study also shows that an optimal size of the spacer fabric exists for achieving minimal peak acceleration under impact at a certain kinetic energy. Experimental validation by drop-weight impact tests demonstrates that the predictions of the dynamic model are in satisfactory agreement with the experimental results. Using the quasi-static compressive data from a simple test, this dynamic model can numerically simulate the full time-response of warp-knitted spacer fabrics under various impact conditions.

Deformation of as-fabricated and helium implanted 100 nm-diameter iron nano-pillars

〈101〉-oriented cylindrical single crystalline Fe samples with diameters of 100nm and heights of 1μm were implanted with 0.36±0.06at% helium throughout their gauge sections. Uniaxial deformation experiments revealed a 40% higher yield and ultimate strengths in tension and a 25% higher yield strength and flow stress at 10% plastic strain in compression for implanted samples compared with as-fabricated ones. Observed tension–compression asymmetry in implanted pillars was attributed to the non-planarity of screw dislocation cores and to twinning-antitwinning deformation typical of bcc metals and the interaction between dislocations and He bubbles. Compressive stress–strain data in both sets of samples had three distinct regimes: (1) elastic loading followed by (2) discrete strain bursts during plastic flow with significant hardening up to strains of 5%, and (3) “steady state” discrete plasticity characterized by nearly-constant average flow stress. Each regime is discussed and explained in terms of competition in the rates of dislocation multiplication and dislocation annihilation.

Grain Boundary Sliding in Aluminum Nano‐Bi‐Crystals Deformed at Room Temperature

Room-temperature uniaxial compressions of 900-nm-diameter aluminum bi-crystals, each containing a high-angle grain boundary with a plane normal inclined at 24° to the loading direction, revealed frictional sliding along the boundary plane to be the dominant deformation mechanism. The top crystallite sheared off as a single unit in the course of compression instead of crystallographic slip and extensive dislocation activity, as would be expected. Compressive stress strain data of deforming nano bicrystals was continuous, in contrast to single crystalline nano structures that show a stochastic stress strain signature, and displayed a peak in stress at the elastic limit of ~ 176 MPa followed by gradual softening and a plateau centered around ~ 125 MPa. An energetics-based physical model, which may explain observed room-temperature grain boundary sliding, in presented, and observations are discussed within the framework of crystalline nano-plasticity and defect microstructure evolution.

High strain-rate compressive behavior and constitutive modeling of selected polymers

The present paper deals with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10−3 to 103 /s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves for four different commercially available extruded polymers are determined on the standard split Hopkinson pressure bar. The low and intermediate strain-rates compressive stress-strain relations are measured in an Instron testing machine. The five parameters for the modified Ramberg-Osgood equation are determined by fitting to the experimental compressive stress-strain data using a least-squares fit. The compressive stress-strain curves at three different strain rates derived from the modified Ramberg-Osgood models are compared with the experimental results. It is shown that the compressive stress-strain behavior during loading process can be successfully predicted by the modified Ramberg-Osgood equation.

High Strain-Rate Compressive Behavior of Bulk Structural Adhesives: Epoxy and Methacrylate Adhesives

The present paper describes the determination of high strain-rate compressive stress-strain loops for bulk specimens of two different epoxy and methacrylate structural adhesives on the standard split Hopkinson pressure bar with a tapered striker bar. The full compressive stress-strain data including unloading process are obtained over a wide range of strain rates from 10-3 to 103/s at room temperature. The effects of strain rate on the initial (secant) modulus, flow stress, dissipation energy and hysteresis loss ratio are studied. The experimental results show that both bulk structural adhesives exhibit highly strain-rate dependent viscoelastic behavior like polymeric materials.

High Strain-Rate Compressive Stress-Strain Loops for Structural Adhesive

The high strain-rate compressive stress-strain loops for bulk specimens of an epoxy structural adhesive are determined on the standard split Hopkinson pressure bar. The compressive stress-strain data including unloading curves are obtained over a wide range of strain rates from 10-3to 103/s. The effects of strain rate on the initial (secant) modulus, flow stress, dissipation energy and hysteresis loss ratio are discussed. The experimental results show that the bulk structural adhesive exhibits dynamic viscoelastic behavior like polymers.

Numerical modeling of uneven thermoplastic polymers behaviour using experimental stress-strain data and pressure dependent von Mises yield criteria to improve design practices

Classical plasticity theories and yield criteria for ductile materials, such as Tresca and von Mises original formulations predict that yielding is independent on the hydrostatic stress state (pressure), which means that tensile and compressive stress-strain behaviours are considered equal and are equally treated. This approach is reasonable for ductile metallic materials but sometimes inaccurate for polymers, which commonly present larger compressive yield strength, therefore being characterized as uneven. Polymer unevenness can be of great interest for mechanical structural design since components that present regions operating under compression can be optimized taking this phenomenon into account. Compressive stress-strain data for polymers are very scarce in the literature, and as a step in this direction this work presents three key-activities: i) four selected polymers were tested under tension and compression to identify unevenness and assess its levels; ii) pressure dependent yield criteria applicable for polymers were briefly reviewed; iii) experimental results were incorporated in adapted design practices using modified yield criteria implemented in optimization and finite element computations. Results show that taking unevenness into account and implementing modified criteria in the numerical techniques for structural calculation can provide mass reductions up to ∼ 38% even with simple geometric changes, while keeping original safety and stiffness levels.

Strain‐hardening modulus of cross‐linked glassy poly(methyl methacrylate)

AbstractThe strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well‐known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010

Mechanical characterization at intermediate strain rates for rate effects on an epoxy syntactic foam

An intermediate strain-rate mechanical testing technique was developed through proper modifications of a hydraulically driven loading frame (MTS 810) and a split Hopkinson pressure bar (SHPB). The modified MTS and SHPB were used to obtain valid stress–strain data for an epoxy syntactic foam at intermediate strain rates in the order from 10 −1 to 10 2 s −1. Additionally, lower and higher strain-rate characterization of the foam material was conducted, such that the compressive stress–strain data of the syntactic epoxy foam were obtained at strain rates from 0.005 to 2150 s −1 without any gap in the intermediate strain-rate range. The syntactic epoxy foam exhibited nonlinear strain-rate dependency of failure strength.

DYNAMIC DEFORMATION BEHAVIOR OF SOFT MATERIAL USING SHPB TECHNIQUE AND PULSE SHAPER

This paper presents a modified Split Hopkinson Pressure Bar (SHPB) technique to obtain compressive stress strain data for NBR rubber materials. An experimental technique with a modified the conventional SHPB has been developed for measuring the compressive stress strain responses of materials with low mechanical impedance and low compressive strengths, such as the rubber and the polymeric material. This paper uses an aluminum pressure bar to achieve a closer impedance match between the pressure bar and the specimen materials. In addition, a pulse shaper is utilized to lengthen the rising time of the incident pulse to ensure dynamic stress equilibrium and homogeneous deformation of NBR rubber materials. It is found that the modified technique can determine the dynamic deformation behavior of rubbers more accurately.

Thickness Effect of Pulse Shaper on Dynamic Stress Equilibrium in the NBR Rubber Specimen

This paper presents an experimental finding in the Split Hopkinson Pressure Bar (SHPB) technique to obtain a better compressive stress strain data for rubber materials. An experimental technique which modifies the conventional SHPB has been developed for measuring the compressive stress strain responses of materials with low mechanical impedance and low compressive strengths such as rubber. This paper uses an all-polymeric pressure bar to achieves a closer impedance match between the pressure bar and the specimen materials. In addition, a pulse shaper is utilized to lengthen the rising time of the incident pulse to ensure stress equilibrium and homogeneous deformation of rubber materials. It is found that the modified technique can determine the dynamic deformation behavior of a rubber more accurately.

Dynamic Deformation Behavior of Rubber (NR/NBR) under High Strain Rate Compressive Loading

This paper presents a modified Split Hopkinson Pressure Bar (SHPB) technique to obtain compressive stress-strain data for rubber materials. An experimental technique that modifies the conventional SHPB has been developed for measuring the dynamic compressive stress-strain responses of rubber materials with low mechanical impedance and low compressive strengths. This paper introduces an all-polymeric pressure bar set-up which achieves a closer impedance match between the pressure bar and the specimen materials. In addition, a pulse shaper is utilized to lengthen the rising time of the incident wave which helps the stress equilibrium and homogeneous deformation of rubber materials. It is found that the modified technique can determine the dynamic deformation behavior of NR and NBR rubber more accurately than those from the conventional SHPB technique.