scholarly journals Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3667
Author(s):  
Yevgeniya Filanova ◽  
Johannes Hauptmann ◽  
Frank Längler ◽  
Konstantin Naumenko
Keyword(s):  
Experimental Data ◽  
Strain Rate ◽  
Axial Strain ◽  
Equivalent Stress ◽  
Small Strain ◽  
Composite Model ◽  
Constitutive Law ◽  
Flow Rule ◽  
Inelastic Behavior ◽  
Temperature Ranges

The aim of this paper is to present experimental data and the constitutive model for the inelastic behavior of polyoxymethylene in wide strain rate and temperature ranges. To capture the non-linearity of the stress responses for both loading and unloading regimes, the composite model of inelastic deformation is utilized and further developed. The equivalent inelastic strain rate is described by the Prandtl–Eyring law, while the temperature dependence is characterized by the modified Arrhenius-type law. Generalized equivalent stress and the flow rule are formulated to capture pressure sensitivity, transverse strain and volumetric strain responses. The results obtained by the constitutive law are compared with experimental data for stress vs. axial strain from standard tension tests as well as with axial and transverse strains measured by digital image correlation. The developed composite model is able to capture the non-linearity of stress–strain curves for complex loading paths within the small strain regime. For higher strains, apart from geometrically non-linear theory, evolution laws for the volume fraction of the constituents should be modified and calibrated. For the small strain regime, the inelastic dilatation is negligible. For higher axial strain values, a decrease in Poisson’s ratio under tension and increase in it under compression are observed. The Drucker–Prager-type equivalent stress and the developed flow rule provide a better description of both the transverse and volumetric strains than that of the classical von Mises–Odqvist flow rules.

A Physically Based Flow Rule for the Simulation of Ti-6Al-4V Forging in the α - β Range

2007 ◽  
Vol 539-543 ◽  
pp. 3661-3666 ◽  
Author(s):  
A. Colin ◽  
Christophe Desrayaud ◽  
Marie Mineur ◽  
Frank Montheillet
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Thermomechanical Processing ◽  
Deformation Behaviour ◽  
True Strain ◽  
Hot Forging ◽  
Constitutive Law ◽  
Flow Rule ◽  
Plastic Energy

The aim of this work is to study the flow instabilities occurring during hot forging of titanium alloy blades. In this view, the viscoplastic deformation behaviour of Ti-6Al-4V alloy is investigated by means of torsion tests under isothermal hot working conditions at temperatures ranging from 800 to 1020 °C and strain rates of 0.01, 0.1 and 1s−1. The thermomechanical processing is performed up to a true strain of 10. The flow stress data are analysed in terms of strain rate and temperature sensitivities. A constitutive equation that relates not only the dependence of the flow stress on strain, strain rate and temperature, but also for the fraction of each phase α and β is proposed. Two mechanical models are compared : the uniform strain rate model (Taylor) and the uniform plastic energy model (IsoW). The usual strain rate sensitivity and activation energy values of Ti-6Al-4V alloy are obtained by fitting the experimental data. Furthermore, specific values of strain rate sensitivities and activation energies are calculated for the α and β phases providing thus a constitutive law based on the physics of the α / β phase diagram. The flow stress is then related to strain by an empirical equation taking into account the flow softening observed after a true strain of 0.5 and the steady state flow reached after a true strain of 4. Comparison of the calculated and measured flow stresses shows that the constitutive equation predicts the experimental results with a reasonable accuracy. The above constitutive equation is then used for simulating forging processes by the finite element method. The calculations exhibit the localisation of deformation produced by shearing effects in the form of the classical X shape.

scholarly journals Small-strain deformation behaviour of a clay at frozen and unfrozen states: A comparative study

2019 ◽  
Vol 92 ◽  
pp. 04001
Author(s):  
Satoshi Nishimura ◽  
Shota Okajima ◽  
Jinyuan Wang ◽  
Bhakta Raj Joshi
Keyword(s):  
Strain Rate ◽  
Axial Strain ◽  
Deformation Behaviour ◽  
Triaxial Compression ◽  
Small Strain ◽  
Small Scale ◽  
High Plasticity ◽  
Compression Tests ◽  
Small Strains ◽  
Displacement Sensors

The small-strain deformation behaviour of frozen high-plasticity clay, and the factors influencing it were investigated through parallel tests at frozen and unfrozen states. The first and second series involved temperature-controlled triaxial compression tests on unfrozen and frozen samples, respectively, with accurate strain measurement with local displacement sensors, fully calibrated for cold environment. The small-strain loading was conducted at different axial strain rates and temperatures. At pre-yield small strains in order of 0.001%, Young's modulus was independent of the strain rate, in a same manner as in unfrozen soils. The strain rate only affected the onset of small-scale yielding and the degradation of stiffness after that. The elastic strain range was greater at lower temperature, but the degree of stress-strain non-linearity seen at small strains remained on the whole similar between frozen and unfrozen states. An interesting feature of the frozen clay's stiffness, also confirmed by third test series adopting bender elements, is that it decreases when the soil is frozen from higher effective stress. A simple model was proposed to explain this feature.

scholarly journals Bounding Surface Elasto-Viscoplasticity: A General Constitutive Framework for Rate-Dependent Geomaterials

2018 ◽  
Author(s):  
Zhenhao Shi ◽  
James Hambleton ◽  
Giuseppe Buscarnera
Keyword(s):  
Strain Rate ◽  
Axial Strain ◽  
Constitutive Law ◽  
Strain Rates ◽  
Bounding Surface ◽  
Rate Dependent ◽  
Wide Range ◽  
Modified Cam Clay ◽  
Constitutive Parameters ◽  
New Framework

A general framework is proposed to incorporate rate and time effects into bounding surface (BS) plasticity models. For this purpose, the elasto-viscoplasticity (EVP) overstress theory is combined with bounding surface modeling techniques. The resulting constitutive framework simply requires the definition of an overstress function through which BS models can be augmented without additional constitutive hypotheses. The new formulation differs from existing rate-dependent bounding surface frameworks in that the strain rate is additively decomposed into elastic and viscoplastic parts, much like classical viscoplasticity. Accordingly, the proposed bounding surface elasto-viscoplasticity (BS-EVP) framework is characterized by two attractive features: (1) the rate-independent limit is naturally recovered at low strain rates; (2) the inelastic strain rate depends exclusively on the current state. To illustrate the advantages of the new framework, a particular BS-EVP constitutive law is formulated by enhancing the Modified Cam-clay model through the proposed theory. From a qualitative standpoint, this simple model shows that the new framework is able to replicate a wide range of time/rate effects occurring at stress levels located strictly inside the bounding surface. From a quantitative standpoint, the calibration of the model for over-consolidated Hong Kong marine clays shows that, despite the use of only six constitutive parameters, the resulting model is able to realistically replicate the undrained shear behavior of clay samples with OCR ranging from 1 to 8, and subjected to axial strain rates spanning from 0.15%/hr to 15%/hr. These promising features demonstrate that the proposed BS-EVP framework represents an ideal platform to model geomaterials characterized by complex past stress history and cyclic stress fluctuations applied at rapidly varying rates.

scholarly journals Small Strain Behavior of Geomaterials: Modelling of Strain Rate Effects

1997 ◽  
Vol 37 (2) ◽  
pp. 127-138 ◽  
Author(s):  
Hervé Di Benedetto ◽  
Fumio Tatsuoka
Keyword(s):  
Strain Rate ◽  
Small Strain ◽  
Strain Rate Effects ◽  
Strain Behavior ◽  
Rate Effects

Strain-Rate Effect on the Tensile Behaviour of High Strength Alloys

2011 ◽  
Vol 82 ◽  
pp. 124-129 ◽  
Author(s):  
Ezio Cadoni ◽  
Matteo Dotta ◽  
Daniele Forni ◽  
Stefano Bianchi
Keyword(s):  
Strain Rate ◽  
Rate Sensitivity ◽  
High Strength ◽  
Constitutive Law ◽  
Tensile Behaviour ◽  
Strain Rates ◽  
Cross Sectional ◽  
Split Hopkinson Tensile Bar ◽  
Wide Range ◽  
First Results

In this paper the first results of the mechanical characterization in tension of two high strength alloys in a wide range of strain rates are presented. Different experimental techniques were used for different strain rates: a universal machine, a Hydro-Pneumatic Machine and a JRC-Split Hopkinson Tensile Bar. The experimental research was developed in the DynaMat laboratory of the University of Applied Sciences of Southern Switzerland. An increase of the stress at a given strain increasing the strain-rate from 10-3 to 103 s-1, a moderate strain-rate sensitivity of the uniform and fracture strain, a poor reduction of the cross-sectional area at fracture with increasing the strain-rate were shown. Based on these experimental results the parameters required by the Johnson-Cook constitutive law were determined.

scholarly journals Development of a Novel Hybrid Unified Viscoplastic Constitutive Model

2015 ◽  
Author(s):  
Luis A. Varela J. ◽  
Calvin M. Stewart
Keyword(s):  
Experimental Data ◽  
Stainless Steel ◽  
Hybrid Model ◽  
Material Constant ◽  
Inelastic Behavior ◽  
Hastelloy X ◽  
Material Constants ◽  
Stainless Steel 304 ◽  
Simulation Results ◽  
Optimal Material

Hastelloy X and stainless steel 304 are alloys widely used in industrial gas turbines components, petrochemical industry and energy generation applications; In the Pressure Vessel and Piping (PVP) industries they are used in nuclear and chemical reactors, pipes and valves applications. Hastelloy X and stainless steel 304 are favored for these types of applications where elevated temperatures are preferred for better systems’ efficiencies; they are favored due to its high strength and corrosion resistance at high temperature levels. A common characteristic of these alloys, is its rate-dependent mechanical behavior which difficult the prediction of the material response for design and simulation purposes. Therefore, a precise unified viscoplastic model capable to describe Hastelloy X and stainless steel 304 behaviors under a variety of loading conditions at high temperatures is needed to allow a better and less conservative design of components. Numerous classical unified viscoplastic models have been proposed in literature, to predict the inelastic behavior of metals under extreme environments. Based on Miller and Walker classical unified constitutive models a novel hybrid unified viscoplastic constitutive model is introduced in the present work, to describe the inelastic behavior caused by creep and fatigue effects at high temperature. The presented hybrid model consists of the combination of the best aspects of Miller and Walker model constitutive equations, with the addition of a damage rate equation which provides a description of the damage evolution and rupture prediction capabilities for Hastelloy X and stainless steel 304. A detailed explanation on the meaning of each material constant is provided, along with its impact on the hybrid model behavior. Material constants were calculated using the recently developed Material Constant Heuristic Optimizer (MACHO) software, to ensure the use of the optimal material constants values. This software uses the simulated annealing algorithm to determine the optimal material constants in a global surface, by comparing numerical simulations to an extensive database of experimental data. To validate the capabilities of the proposed hybrid model, numerical simulation results are compared to a broad range of experimental data at different stress levels and strain amplitudes; besides the consideration of two alloys in the present work, would demonstrate the model’s capabilities and flexibility to model multiple alloys behavior. Finally a quantitative analysis is provided to determine the percentage error and coefficient of determination between the experimental data and numerical simulation results to estimate the efficiency of the proposed hybrid model.

Mesodamage Evolution in Polycrystals

2005 ◽  
Vol 127 (2) ◽  
pp. 214-221 ◽  
Author(s):  
M. Chadli ◽  
A. Abdul-Latif
Keyword(s):  
Fatigue Life ◽  
Micromechanical Model ◽  
Small Strain ◽  
Cyclic Stress ◽  
Damage Variable ◽  
Thermodynamic Force ◽  
Inelastic Behavior ◽  
Loading Paths ◽  
Localized Plastic Deformation ◽  
Phase Angles

A micromechanical model of damaged elasto-inelastic behavior is proposed to predict the plastic fatigue life for fcc metallic polycrystals under multiaxial loading paths. This model is expressed in the time-dependent plasticity for a small strain assumption. In order to generalize and then to increase the model applicability (with respect to other works of the author) in describing the cyclic stress-strain evolution during plastic fatigue, it is therefore assumed that a damage variable initiates and then evolves at the grain level where the phenomenon of the localized plastic deformation occurs. The associated thermodynamic force of the damage variable is determined as a total granular energy (elastic and inelastic). The transition of the elastic strain from the single to the polycrystal, which is classically performed by averaging procedures in this type of modeling, is modified due to the coupling of such a strain with damage. The developed model is tested under different multiaxial cyclic loading situations (tension-compression and tension-torsion with different out-of-phase angles). The effects the loading paths and the grains aggregate type on the fatigue life are appropriately investigated. It is demonstrated that the model can correctly describe the overall and local damaged behavior of polycrystals.

A New Elasto-Plastic Critical State Model RU+MCC for Overconsolidated Soil

2016 ◽  
Vol 837 ◽  
pp. 68-74
Author(s):  
Rafal Uliniarz
Keyword(s):  
Critical State ◽  
Soil Mechanics ◽  
Small Strain ◽  
Computer Code ◽  
Constitutive Law ◽  
Isotropic Hardening ◽  
Loading Test ◽  
Modified Cam Clay ◽  
Soil Behaviour ◽  
Cam Clay

The paper presents a reasonably advanced constitutive law for soil – a hybrid of the Modified Cam Clay and a new RU development. The Modified Cam Clay model is an isotropic hardening elasto – plastic model originated by Burland in 1967 [1] within the critical state soil mechanics. This model describes realistically mechanical soil behaviour in normal consolidation states. The other one is designed to ensure more adequate soil responses to reloading paths, particularly in the range of small strains. The RU+MCC model has been implemented in the FEM computer code Z_SOIL.pc. To test the influence of the small strain nonlinearity on soil – structure interaction as well as to exhibit the ability of the proposed model to simulate realistically this effect, a comparative study based on the FEM solution has been carried out. As a benchmark a trial loading test of strip footing was used.

scholarly journals Behavior of Dynamic Strain Aging in Zr-1.5Nb-0.4Sn-0.2Fe-0.1Cr Alloy Strip

2021 ◽  
Vol 59 (1) ◽  
pp. 8-13
Author(s):  
Il-Hyun Kim ◽  
Myung-Ho Lee ◽  
Yang-Il Jung ◽  
Hyun-Gil Kim ◽  
Jae-Il Jang
Keyword(s):  
Tensile Test ◽  
Strain Rate ◽  
Dynamic Strain Aging ◽  
Strain Aging ◽  
Rolling Direction ◽  
Rate Sensitivity ◽  
Dynamic Strain ◽  
Alloy Strip ◽  
Lower Strain ◽  
Temperature Ranges

The behavior of dynamic strain aging (DSA) in a Zr-1.5Nb-0.4Sn-0.2Fe-0.1Cr alloy strip was investigated at temperature ranges of 25–600 °C via a tensile test. The tensile test was performed at two different strain rates 8.33 × 10<sup>-5</sup> and 1.67 × 10<sup>-2</sup> s<sup>-1</sup>. The shear stress of the alloy strip revealed a linear dependency on the test temperature when the specimens were tested under a higher strain rate (1.67 × 10<sup>-2</sup> s<sup>-1</sup>). However, the linear relationship was broken due to DSA when the samples were deformed under a lower strain rate (8.33 × 10<sup>-5</sup> s<sup>-1</sup>). The discrepancy was most significant at 400 °C. The trend in DSA behavior was similar irrespective of the orientation of the samples, i.e., rolling direction (RD) or transverse direction (TD). However, the effect of DSA was larger in the TD samples than the RD samples. The phenomena were interpreted to the variation in work hardening exponents and strain rate sensitivity. The value of the exponent decreased from 0.14 to 0.08 along a RD and from 0.1 to 0.07 along a TD, respectively. However, the smallest value was observed at 400–500 °C irrespective of the specimen orientation, which is consistent with the DSA behavior. It is suggested that the DSA was caused by an interaction of moving dislocations with solute atoms typically oxygen.

A Comprehensive Energy Formulation for General Nonlinear Material Continua

1997 ◽  
Vol 64 (2) ◽  
pp. 353-360 ◽  
Author(s):  
A. Carini ◽  
O. De Donato
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Small Strain ◽  
Constitutive Law ◽  
Nonlinear Material ◽  
Total Potential ◽  
Initial Boundary Value ◽  
Energy Formulation ◽  
The Continuum

By specialization to the continuum problem of a general formulation of the initial/boundary value problem for every nonpotential operator (Tonti, 1984) and by virtue of a suitable choice of the “integrating operator,” a comprehensive energy formulation is established. Referring to the small strain and displacement case in the presence of any inelastic generally nonlinear constitutive law, provided that it is differentiable, this formulation allows us to derive extensions of well-known principles of elasticity (Hu-Washizu, Hellinger-Reissner, total potential energy, and complementary energy). An illustrative example is given. Peculiar properties of the formulation are the energy characterization of the functional and the use of Green functions of the same problem in the elastic range for every inelastic, generally nonlinear material considered.

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