Uniaxial stress-strain curves from a bending test

Mayville, Ronald A.; Finnie, I.

doi:10.1007/bf02326357

Cited by 51 publications

(52 citation statements)

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“…The implementation of bending experiments to extract elastic and plastic behavior from brittle or complex materials goes back to the beginning of the twentieth century as reviewed by Mayville and Finnie [7]. Mayville and Finnie use the analysis of Herbert [8] to measure the stress strain behavior of different materials by four-point bending and compare the results with conventional uniaxial tensile tests.…”

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confidence: 99%

Mechanical Characterization of Coatings Using Microbeam Bending and Digital Image Correlation Techniques

2008

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A new technique for characterizing end-supported microbeams of coating materials is presented. Microbeams are fabricated using micro-EDM machining to isolate the material under investigation from the underlying substrate. Three-and four-point bending is realized by a custom-built microspecimen testing system, and digital image correlation is employed to capture full-field strains and displacements in theses microbeams. These experiments provide the foundation for the use of finite element modeling and inverse methods to determine the mechanical properties (elastic moduli, strength, interfacial toughness) of the coatings. Here, the experimental details of the microbeam bending experiments are explained, discussed and illustrated through application to a multilayered metal/oxide/ ceramic thermal barrier coating system commonly used in aero-turbines.

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Section: Introductionmentioning

confidence: 99%

Mechanical Characterization of Coatings Using Microbeam Bending and Digital Image Correlation Techniques

2008

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“…which are equal to the expressions derived by Mayville and Finnie in 1981 [2]. In these incremental forms the causal relationship between bending curves and calculated s-s curves is not easy to grasp.…”

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confidence: 56%

“…That is, the calculation is sensitive to the derivative of P -ϵ curves, which means that a high-order precision is needed in the bending experiment. This oscillation was not found in the previous study, since the calculation of s-s curves was carried out in a few points [2]. Some data processing to smooth the P -ϵ curves may be effective to remove oscillation originating from instrumental errors.…”

mentioning

confidence: 70%

“…This oscillation was not found in the previous study, since the calculation of s-s curves was carried out in a few points [2]. Some data processing to smooth the P -ϵ curves may be effective to remove oscillation originating from instrumental errors.…”

mentioning

confidence: 70%

“…This classical subject was discussed by Nadai [1]. Later, Mayville and Finnie studied this problem, and derived a formula [2]. Despite the potential of the formula and also the usefulness of bending test, very few application has been found.…”

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Four-Point Bending Test of Determining Stress-Strain Curves Asymmetric between Tension and Compression

2013

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Keywords inverse problem · plasticity · four-point bending A method of determining both uniaxial tension and compression stressstrain curves from the result of a single four-point bending test was demonstrated. Stress-strain curves of magnesium showing tension-compression asymmetry due to twinning deformation and those of an S45C steel due to the Bauschinger effect were calculated. The Mayville-Finnie equation was modified slightly for this calculation. The calculation is sensitive to small change in the derivative of bending curve, revealing an aspect of inverse problem.An inverse problem in elasto-plastic bending of a material may be to determine uniaxial stress-strain (s-s) curve of the material. This classical subject was discussed by Nadai [1]. Later, Mayville and Finnie studied this problem, and derived a formula [2]. Despite the potential of the formula and also the usefulness of bending test, very few application has been found. Let us consider four-point bending of a prismatic bar (Fig.1). The bar is simply supported at points A and B, and a load P/2 is subjected at points C and D equally. Pure bending with the radius of curvature ρ occurs between C and D, where a constant bending moment of M = P d/2 is subjected. The bending strains of the outermost surfaces ϵ 1 (compression) and ϵ 2 (tension) are measured with two pieces of strain gauge. Accordingly, two curves of bending load vs. bending strain relation (P -ϵ curves) are obtained: ϵ 1 = ϵ 1 (P ) and ϵ 2 = ϵ 2 (P ). The bar has a constant rectangular cross section, where a local y coordinate is taken as in Fig.2. Yield stress in compression is Y 1 and in tension Y 2 . A neutral axis NN is located at y = y 0 . When s-s curves are asymmetric between tension and compression, the neutral axis is away from the centroid axis at y = h/2 while bending.A P -ϵ curve can be derived readily from the exact shape of s-s curve, if it is known. This is a forward problem in bending. For example, a material with an ideal elastic-perfect plastic s-s behavior illustrated in Fig.3(a) shows P-ϵ curves of Fig.3(b). The calculation was carried out by assuming that the modulus of elasticity E was 100 GPa, the yield stresses Y 1 in compression, 100MPa, Y 2 in tension, 200 MPa, and the dimensions, b=5 mm, h=1 mm, d=10 mm. Properties of P-ϵ curves listed below are common to any elasto-plastic(i) The linear relationship in elastic bending is given by(ii) When the compression side starts yielding, tension and compression curves branch off from the linear relationship at a point where the load is P 1 and the strain isTitle Suppressed Due to Excessive Length 3 (iii) When the tension side starts yielding, the two curves change the slopes at a point where the load is P 2 and the strain isThe inverse problem is to determine s-s curves from the result of bending.Without solving the problem, we can determine the values of E, Y 1 and Y 2 from P-ϵ curves. Let us start from the P-ϵ curves of Fig.3(b). The slope of linear relationship determines E as 100GPa from Eq.(1). The first and second ...

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Identification and estimation of constitutive parameters for material laws in elastoplasticity

et al. 2007

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MSC (2000) 49Q12, 74P10, 74S05The paper summarizes the comprehensive experience of the authors in the numerical identification and estimation of parameters for anisotropic elastoplastic material laws analyzing inhomogeneous mechanical fields. Generally, the constitutive model under consideration represents a system of differential and algebraic equations. It distinguishes itself by a strictly thermodynamically consistent foundation, and an identical structure in case of small as well as finite deformations. Different rules for the evolution of internal variables describing various hardening effects are proposed. The nonlinear inverse problem of the identification of material parameters is solved with deterministic optimization methods. Basically, the least squares type objective function contains several local and global variables for the comparison of experimental and numerical data. Within this context, the numerical values of the comparative quantities are calculated either using the local integration of the initial value problem at suitably chosen material points or analyzing the entire initial-boundary value problem (e.g. with the Finite Element Method). In order to obtain the gradient of the objective function within the framework of a sensitivity analysis a semianalytical approach based on the implicit differentiation of the equilibrium conditions and the discretized constitutive relations is presented. The numerical algorithms for the direct as well as the inverse problem are implemented into in-house Finite Element codes. Some examples based on real and numerical experiments analyzing selected constitutive approaches are presented.

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Uniaxial stress-strain curves from a bending test

Cited by 51 publications

References 1 publication

Mechanical Characterization of Coatings Using Microbeam Bending and Digital Image Correlation Techniques

Mechanical Characterization of Coatings Using Microbeam Bending and Digital Image Correlation Techniques

Four-Point Bending Test of Determining Stress-Strain Curves Asymmetric between Tension and Compression

Identification and estimation of constitutive parameters for material laws in elastoplasticity

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