Three-Dimensional Constraint Effects on the Slitting Method for Measuring Residual Stress

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
C. Can Aydıner ◽  
Michael B. Prime
Keyword(s):  
Residual Stress ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Out Of Plane ◽  
Sample Width ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Calibration Coefficients

The incremental slitting or crack compliance method determines a residual stress profile from strain measurements taken as a slit is incrementally extended into the material. To date, the inverse calculation of residual stress from strain data conveniently adopts a two-dimensional, plane strain approximation for the calibration coefficients. This study provides the first characterization of the errors caused by the 2D approximation, which is a concern since inverse analyses tend to magnify such errors. Three-dimensional finite element calculations are used to study the effect of the out-of-plane dimension through a large scale parametric study over the sample width, Poisson's ratio, and strain gauge width. Energy and strain response to point loads at every slit depth is calculated giving pointwise measures of the out-of-plane constraint level (the scale between plane strain and plane stress). It is shown that the pointwise level of constraint varies with slit depth, a factor that makes the effective constraint a function of the residual stress to be measured. Using a series expansion inverse solution, the 3D simulated data of a representative set of residual stress profiles are reduced with 2D calibration coefficients to yield the error in stress. The sample width below which it is better to use plane stress compliances than plane strain is shown to be about 0.7 times the sample thickness; however, even using the better approximation, the rms stress errors sometimes still exceed 3% with peak errors exceeding 6% for Poisson's ratio 0.3, and errors increase sharply for larger Poisson's ratios. The error is significant, yet, error magnification from the inverse analysis in this case is mild compared to, e.g., plasticity based errors. Finally, a scalar correction (effective constraint) over the plane-strain coefficients is derived to minimize the root-mean-square (rms) stress error. Using the posed scalar correction, the error can be further cut in half for all widths and Poisson's ratios.

scholarly journals Bond-based peridynamics: A tale of two Poisson's ratios

2019 ◽  
Author(s):  
Jeremy Trageser ◽  
Pablo Seleson
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Materials ◽  
Stress Models ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

This paper explores the restrictions imposed by bond-based peridynamics, particularly with respect to plane strain and plane stress models. We begin with a review of the derivations in [2] wherein for isotropic materials a Poisson's ratio restriction of 1/4 for plane strain and 1/3 for plane stress is deduced. Next, we show Cauchy's relations are an intrinsic limitation of bond-based peridynamics and specialize this result to plane strain and plane stress models, generalizing the results of [2] and demonstrating the Poisson's ratio restrictions in [2] are simply a consequence of Cauchy's relations. We conclude with a discussion of the validity of peridynamic plane strain and plane stress models formulated from two-dimensional bond-based peridynamic models.

scholarly journals Regularly configured structures with polygonal prisms for three-dimensional auxetic behaviour

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160926 ◽  
Author(s):  
Junhyun Kim ◽  
Dongheok Shin ◽  
Do-Sik Yoo ◽  
Kyoungsik Kim
Keyword(s):  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Numerical Verification ◽  
Geometric Conditions ◽  
Unit Cells ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

We report here structures, constructed with regular polygonal prisms, that exhibit negative Poisson’s ratios. In particular, we show how we can construct such a structure with regular n -gonal prism-shaped unit cells that are again built with regular n -gonal component prisms. First, we show that the only three possible values for n are 3, 4 and 6 and then discuss how we construct the unit cell again with regular n -gonal component prisms. Then, we derive Poisson’s ratio formula for each of the three structures and show, by analysis and numerical verification, that the structures possess negative Poisson’s ratio under certain geometric conditions.

Residual Stress in EB-PVD Thermal Barrier Coatings

2006 ◽  
Vol 524-525 ◽  
pp. 879-884 ◽  
Author(s):  
Kenji Suzuki ◽  
Keisuke Tanaka ◽  
Takahisa Shobu
Keyword(s):  
Residual Stress ◽  
Plane Strain ◽  
Plane Stress ◽  
Physical Vapor Deposition ◽  
Preferred Orientation ◽  
X Rays ◽  
Scanning Method ◽  
Bond Coating ◽  
Out Of Plane ◽  
Steep Decrease

A NiCoCrAlY bond coating was low-pressure plasma sprayed on a stainless steel sub- strate. Zirconia with 8 wt% yttria was deposited on the bond coating using an electron beam-physical vapor deposition (EB-PVD) method. The top coating had the preferred orientation with the h111i axis direction perpendicular to the coating plane. The distribution of the in-plane residual stress in the top coating was measured using laboratory Cr-K X-rays with a progressive layer removal method. The value of the in-plane stresses was determined by the sin2 method after the separation of the 133 and 331 peaks. The distribution of the out-of-plane strain in the top coating was measured using the strain scanning method with hard synchrotron X-rays. The out-of-plane strain was obtained from the 333 peak which had strong intensity due to the preferred orientation. The measured value of the in-plane stress in the top coating was a large compression, and showed a steep decrease near the in- terface between the top and the bond coatings. The distribution of the out-of-plane stress showed a compression, and its magnitude was smaller than that of the in-plane stress.

Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading

1968 ◽  
Vol 35 (3) ◽  
pp. 460-466 ◽  
Author(s):  
David B. Bogy
Keyword(s):  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Shear Loading ◽  
The Other ◽  
Stress Fields ◽  
Shear Moduli ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The plane-strain and generalized plane stress problems of two materially dissimilar orthogonal elastic wedges, which are bonded together on one of their faces while arbitrary normal and shearing tractions are prescribed on their remaining faces, are treated within the theory of classical elastostatics. The asymptotic behavior of the solution in the vicinity of the intersection of the bonded and loaded planes is investigated. The stress fields are found to be singular there with singularities of the type r−α, where α depends on the ratio of the two shear moduli and on the two Poisson’s ratios. This dependence is shown graphically for physically relevant values of the elastic constants. The largest value of α for the range of constants considered is 0.311 and occurs when one material is rigid and the other is incompressible.

scholarly journals Giant negative Poisson’s ratio in two-dimensional V-shaped materials

2021 ◽  
Author(s):  
Xikui Ma ◽  
Jian Liu ◽  
Yingcai Fan ◽  
Weifeng Li ◽  
Jifan Hu ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Two Dimensional ◽  
Auxetic Materials ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Two-dimensional (2D) auxetic materials with exceptional negative Poisson’s ratios (NPR) are drawing increasing interest due to the potentials in medicine, fasteners, tougher composites and many other applications. Improving the auxetic...

scholarly journals Non-Auxetic Mechanical Metamaterials

Materials ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 635 ◽  
Author(s):  
Christa de Jonge ◽  
Helena Kolken ◽  
Amir Zadpoor
Keyword(s):  
Mechanical Properties ◽  
Yield Stress ◽  
Fatigue Behavior ◽  
Analytical Data ◽  
Three Dimensional ◽  
Mechanical Metamaterials ◽  
Macro Scale ◽  
Unit Cells ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The concept of “mechanical metamaterials” has become increasingly popular, since their macro-scale characteristics can be designed to exhibit unusual combinations of mechanical properties on the micro-scale. The advances in additive manufacturing (AM, three-dimensional printing) techniques have boosted the fabrication of these mechanical metamaterials by facilitating a precise control over their micro-architecture. Although mechanical metamaterials with negative Poisson’s ratios (i.e., auxetic metamaterials) have received much attention before and have been reviewed multiple times, no comparable review exists for architected materials with positive Poisson’s ratios. Therefore, this review will focus on the topology-property relationships of non-auxetic mechanical metamaterials in general and five topological designs in particular. These include the designs based on the diamond, cube, truncated cube, rhombic dodecahedron, and the truncated cuboctahedron unit cells. We reviewed the mechanical properties and fatigue behavior of these architected materials, while considering the effects of other factors such as those of the AM process. In addition, we systematically analyzed the experimental, computational, and analytical data and solutions available in the literature for the titanium alloy Ti-6Al-4V. Compression dominated lattices, such as the (truncated) cube, showed the highest mechanical properties. All of the proposed unit cells showed a normalized fatigue strength below that of solid titanium (i.e., 40% of the yield stress), in the range of 12–36% of their yield stress. The unit cells discussed in this review could potentially be applied in bone-mimicking porous structures.

Multilayer Composite Materials with Non-Usual Poisson's Ratios

2007 ◽  
Vol 555 ◽  
pp. 545-552 ◽  
Author(s):  
E.H. Harkati ◽  
Z. Azari ◽  
P. Jodin ◽  
A. Bezazi
Keyword(s):  
Composite Material ◽  
Composite Materials ◽  
Poisson’S Ratio ◽  
Cellular Materials ◽  
Poisson's Ratio ◽  
Multilayer Composite ◽  
Computer Programme ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Most of usual materials exhibit Poisson's ratio comprised between 0 and 0.5. But, for some kind of cellular materials, or for some stacking sequences of unidirectional plies, a composite material can exhibit negative or greater than 0.5 Poisson's ratios. In this paper, a study of different stacking sequences such as [±β/±θ]s plies made from highly anisotropic fibre pre-preg is presented. A special computer programme has been developed for this purpose. Eighteen stacking sequences, including the [±θ] ones, have been computed. The results show that at least one of Poisson's ratios varies between -0.8 to +0.4. Such kind of materials may find applications for particular cases, as their strength is significantly increased by this phenomenon.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

2007 ◽  
Vol 353-358 ◽  
pp. 74-77
Author(s):  
Zheng Yang ◽  
Chong Du Cho ◽  
Ting Ya Su ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Stress Concentration ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

The Effect of Fiber Microstructure on the Observed Poisson’s Ratio of Tendon and Ligament Tissue

2008 ◽  
Author(s):  
Shawn P. Reese ◽  
Steve A. Maas ◽  
Heath A. Henninger ◽  
Jeffrey A. Weiss
Keyword(s):  
Poisson’S Ratio ◽  
Collagen Fiber ◽  
Poisson's Ratio ◽  
Fiber Direction ◽  
Exact Nature ◽  
Tendon Tissue ◽  
Element Analysis ◽  
The Relationship ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

During tensile testing along the predominant collagen fiber direction, ligament and tendon tissue exhibit large Poisson’s ratios ranging from 1.3 in capsular ligament to 2.98 in flexor tendon [1][2]. Although the microstructure of these tissues (especially fiber crimp) has been characterized, the relationship between microstructure and Poisson’s ratio is relatively unexplored. There has been debate regarding the exact nature of the characteristic crimp within tendon fibers, however the two views most present in the literature are that of planar crimp and helical crimp. The aim of this study was to perform a finite element analysis on prototypical models of fibril bundles for both forms of crimp under tensile loading conditions. It was hypothesized that planar crimp alone would be insufficient for generating large Poisson’s ratios, and that some other microstructure (such as a helix) would be required.

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