Enhanced measurement of strain distributions

A theoretical approach is presented that uses multiple strain gages to accurately measure complicated strain distributions. The technique is based on the method of weighted residuals in conjunction with measured strain data and is applicable for arbitrary in-plane strain distributions. Conventional measurements using strain gages are shown to represent a particular case of the approach presented. The experimental characterization of unidimensional strain fields is discussed in detail. Two approaches are presented; these are based on linear and quadratic approximations of the strain field. The strain distribution for two important practical problems is evaluated assuming ideal conditions to assess the performance of the proposed approach. In both cases, the simulated results demonstrate that measurement error resulting from the finite size of a strain gage may be reduced. That is, a larger strain gage may be used for a given maximum admissible error. The method also allows a minimal error of measured nonlinear strains.     

Torsion of cylindrical bodies with varying strain properties

We analyze the results of experimental studies of effective strain properties of damaged, porous, and other inhomogeneous materials and study the main laws of their behavior under strain. We consider the possible versions of constitutive relations taking account of the dependence of the properties of the media under study on the loading conditions or the strain conditions and the relations between the shear and bulk strains. Since the traditional statement of the torsion problems for bodies with such properties cannot be used, we analyze the strain consistency equations and the relations between the strains and displacements in cylindrical coordinates and obtain expressions for the displacements in an appropriate generalized form, which can be used not only for the torsion problems. We study how the distributions of displacements, strains, and stresses under torsion depend on the parameter characterizing the susceptibility of the material strain properties to variations in the stress state type. We show that, in the case of torsion of a cylinder of circular cross-section, there is no deplanation of the cross-section, just as in the classical solution, but the distributions of displacements, strains, and stresses significantly differ from the well-known solutions.     

Transient strain and temperature distributions in long circular cylinders cooled by emission of thermal radiation

This paper describes techniques used to experimentally and analytically determine temperature and strain distributions produced by radiative cooling of long circular cyclinders. Analytical results were obtained by finite-difference techniques. The low-level dynamic thermal strains, measured by means of embedded strain gages, agreed with the predicted values within acceptable limits. Results are presented for the highest strain level and the highest temperature for which the properties of the model were known.     

Predicting the mechanical behavior of two-phase materials with cellular automata

A new mechanical model is proposed to predict the mechanical behavior of inhomogeneous materials. The simple case of an aggregate of two linearly viscous phases submitted to plane strain is addressed here. Calculations involve the Eshelby localization relationships associated with a Walpole-type averaging procedure. When the grains are equiaxed, derivations are entirely analytical, which allows the proposed method to be simply compared with the classical Hashin-Shtrikman lower and upper bounds and the self-consistent model. When large strains are considered, the model is used to predict numerically the overall stress-strain relationships. Significant morphological hardening or softening is shown to occur with increasing strain, depending on the initially equiaxed or elongated grain shapes. Finally, the local distributions of strains, and thus the development of strain inhomogeneities, are also predicted by the model.     

Shear banding analysis of geomaterials by strain gradient enhanced damage model

Shear band localization is investigated by a strain-gradient-enhanced damage model for quasi-brittle geomaterials. This model introduces the strain gradients and their higher-order conjugate stresses into the framework of continuum damage mechanics. The influence of the strain gradients on the constitutive behaviour is taken into account through a generalized damage evolutionary law. A weak-form variational principle is employed to address the additional boundary conditions introduced by the incorporation of the strain gradients and the conjugate higher-order stresses. Damage localization under simple shear condition is analytically investigated by using the theory of discontinuous bifurcation and the concept of the second-order characteristic surface. Analytical solutions for the distributions of strain rates and strain gradient rates, as well as the band width of localised damage are found. Numerical analysis demonstrates the shear band width is proportionally related to the internal length scale through a coefficient function of Poisson’s ratio and a parameter representing the shape of uniaxial stress–strain curve. It is also shown that the obtained distributions of strains and strain gradients are well in accordance with the underlying assumptions for the second-order discontinuous shear band boundary and the weak discontinuous bifurcation theory.     

Elastoplastic state of flexible conical shells with a circular hole under axial tension

The elastoplastic state of thin conical shells with a circular hole is analyzed assuming finite deflections. The distributions of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress–strain state of shells around the hole under axial tension is analyzed taking into account two nonlinear factors. The numerical results are presented as plots and tables     

Orientation dependence of stress distributions in polycrystals deforming elastoplastically under biaxial loadings

The influence of biaxiality of the loading on the crystallographic orientation dependence of crystal stress distributions is examined for polycrystalline solids deformed well into the elastoplastic regime. The examination is couched in terms of two decompositions of the stress. The first is a split of the tensor into its hydrostatic and deviatoric components; the second is a spectral decomposition of the deviatoric stress from which we express the relative values of the principal components as a function of the biaxiality of the stress. Using the framework provided by these decompositions, we investigate trends observed in the lattice strains in polycrystals subjected to biaxial loadings, comparing strains measured by neutron diffraction with finite element simulations. We conclude by showing how the orientation dependence of the stress distributions is influenced by the load biaxiality and by connecting features of the distributions to the elastic and plastic properties of the crystals. Implications of the results are discussed relative to the modeling of strain hardening and defect initiation.     

Full Field Strain Measurement of Resistant Spot Welds Using 3D Image Correlation Systems

This paper describes local strain measurements of electrical resistance spot welds for three sheet stack-ups of Dual Phase (DP600) and Mild steel under quasi-static tensile loading. The experiments were designed to measure local strain distributions at the vicinity of the spot welds using a modified tensile-shear specimen geometry that allows a strain measurement system to access such area. The electrode tip type used was B-nose, and surface indentation levels were 30% and 50% of the sheet thickness. Local strains at critical locations in resistance spot welds were measured using non-contact 3D image correlation systems (ARAMIS) during quasi-static tension tests. The measured local strains were also compared with results offered by a finite element analysis.     

The micro-connection of the second-order moiré fringes and its order determination,and the determination of the boundary strains

The micro-connection method for determining the centre lines of second-order moiré fringes presented in this paper can enhance the accuracy in measuring strain fields, and generally can determine the absolute order of the second-order moiré fringes. The strain data obtained from curved beam experiment are in good accordance with theory. The relationship between the second-order moiré fringe and the strains at the specific points of the specimen is derived. Hence a reciprocate shift method is presented for determining strain distributions in the non-overlapping region of the shifted moiré patterns, (usually in the region of specimen where no second-order moiré fringes occur is the boundary region).     

横观各向同性介质中椭圆夹杂受非弹性剪切变形引起的弹性场的确定

本文求解了横观各向同性介质中椭圆夹杂内受非弹性剪切变形引起的弹性场。采用各向异性弹性力学平面问题的复变函数解法,结合保角变换,获得夹杂内应变能和基体内边界的应力分布和相应的应变能的表达式。进一步,根据最小应变能原理,获得表征夹杂平衡边界的两个特征剪切应变,从而得到了弹性场的解析解。通过应力转换关系,验证了应力解满足夹杂边界上法向正应力和剪应力的连续条件,表明了该解的正确性。本文解可用于复合材料断裂强度的分析中。     

A nonlinear composite shell theory

A general nonlinear theory for the dynamics of elastic anisotropic circular cylindrical shells undergoing small strains and moderate-rotation vibrations is presented. The theory fully accounts for extensionality and geometric nonlinearities by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvatures and strain-displacement expressions that contain the von Karman strains as a special case. Moreover, the linear part of the theory contains, as special cases, most of the classical linear theories when appropriate stress resultants and couples are defined. Parabolic distributions of the transverse shear strains are accounted for by using a third-order theory and hence shear correction factors are not required. Five third-order nonlinear partial differential equations describing the extension, bending, and shear vibrations of shells are obtained using the principle of virtual work and an asymptotic analysis. These equations show that laminated shells display linear elastic and nonlinear geometric couplings among all motions.     

Development of a machine integrated strain-based contact force sensor for pad foot soil compactors

An investigation was undertaken to explore the use of measurable pad strains on a non-vibratory pad foot roller to provide real time continuous evidence of compaction and contact force. Individual pads were instrumented with strain gages in a pattern chosen based on pad finite element analysis (FEA). Different pad–soil contact stress distributions were modeled to simulate a range of soil conditions. The FEA revealed that the contact stress distribution has a significant influence on the observed pad strain field, suggesting soil specific interpretation of pad strains in order to determine contact force. Results from uniaxial laboratory testing of pad loading on dry sand verified the FEA, i.e., experimental strains generally matched within 15% of FEA strains. The contact stress distribution was measured using tactile pressure sensors and found to be moderately parabolic. A soil specific empirical calibration factor relating vertical sidewall strains to contact force was determined. Field testing was performed on the dry sand with multiple instrumented pads installed on a Caterpillar CP56 roller. Pad strain magnitudes increased up to 250% during compaction from repeated passes of the roller. Using the empirical calibration factor, the estimated contact force was shown to increase with compaction, represented by the independently-measured soil unit weight.     

Three dimensional microstructural effects on plane strain ductile crack growth

Ductile crack growth under mode I, plane strain, small scale yielding conditions is analyzed. Overall plane strain loading is prescribed, but a full 3D analysis is carried out to model three dimensional microstructural effects. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model the material. Two populations of second-phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and the effects of different three dimensional distributions on the crack path and on the overall crack growth rate are analyzed. For comparison purposes, a two dimensional distribution of cylindrical inclusions is analyzed. Crack growth occurs off the initial crack plane in all 3D computations, whereas straight ahead crack growth occurs with the two dimensional cylindrical inclusions. As a consequence, the three dimensional distributions of spherical inclusions exhibit an increased crack growth resistance as compared to the two dimensional distribution of cylindrical inclusions.     

Solutions of some simple boundary value problems within the context of a new class of elastic materials

Some simple boundary value problems are studied, for a new class of elastic materials, wherein deformations are expressed as non-linear functions of the stresses. Problems involving ‘homogeneous’ stress distributions and one-dimensional stress distributions are considered. For such problems, deformations are calculated corresponding to the assumed stress distributions. In some of the situations, it is found that non-unique solutions are possible. Interestingly, non-monotonic response of the deformation is possible corresponding to monotonic increase in loading. For a subclass of models, the strain-stress relationship leads to a pronounced strain-gradient concentration domain in the body in that the strains increase tremendously with the stress for small range of the stress (or put differently, the gradient of the strain with respect to the stress is very large in a narrow domain), and they remain practically constant as the stress increases further. Most importantly, we find that for a large subclass of the models considered, the strain remains bounded as the stresses become arbitrarily large, an impossibility in the case of the classical linearized elastic model. This last result has relevance to important problems in which singularities in stresses develop, such as fracture mechanics and other problems involving the application of concentrated loads.     

Quantification of the Dynamic Compressive Response of Two Ottawa Sands

Two types of Ottawa sand (ASTM C778 #20–30 graded sand, denoted OS1, and C109 ASTM #C778 graded sand, denoted OS2) with different particle size distributions were tested in a series of dynamic uniaxial strain experiments using a modified split Hopkinson pressure bar (SHPB) system. The pulse shaper technique was employed to achieve the dynamic force balance and constant strain rate in the sand specimen. The effects of the strain rate, initial void ratio and moisture on the dynamic compression response of sand were examined. Two types of dynamic behavior occurred in the dry sand: solid-like and fluid-like behavior. The OS1 samples exhibited a fluid-like response at all initial void ratios, whereas the OS2 samples exhibited a solid-like response for all void ratios. This difference between the two sands may be due to the difference in the particular size distributions of OS1 and OS2. The initial elastic response of the dry sand samples seemed to be independent of the strain rate. The strain rate effects became more apparent after particle crushing and particle rearrangement began. Under a high degree of saturation, the strain rate effects were immediately apparent, even at lower strains. The dynamic response of sand was remarkably linear until the peak strain was reached.     

On the use of electrical-resistance metallic foil strain gages for measuring large dynamic plastic deformation

The use of electrical-resistance metallic foil strain gages for measuring large plastic strain in dynamic experiments in studied. The maximum nominal strains obtained in this investigation are 35 percent in compression, 25 percent in tension. A linear variation of gage factor with strain is found in this range. The corrected maximum strains are in excellent agreement with permanent strains measured after the tests. Thus foil strain gages can be effectively used to measure the large dynamic plastic strains.     

Experimental analysis of rolling contact stresses in a viscoelastic strip

An experimental approach to two-dimensional, viscoelastic, steadily moving rolling contact is described. The photoviscoelastic technique is employed for the analysis of rolling contact stresses between a viscoelastic plate and a rigid rolling cylinder in which the principal axes of stress, strain and birefringence are not coincident with each other. Using an elliptically polarized white light, the distribution of isochromatic fringe order and the principal axes of birefringence at an instant are determined from a single photoviscoelastic image. The time variations of the differences of the principal stresses and strains, as well as their directions, are obtained by use of the optical constitutive equations of photoviscoelasticity. The experimental results involving the time variation of the stresses around the contact surface and their distributions are analyzed.     

Sensitivity of the shear gage to normal strains

This paper documents an experimental study that was conducted to demonstrate the sensitivity of the shear gage to the presence of normal strains. The shear gage is a specially designed strain gage rosette that measures the average shear strain in the test section of notched specimens such as the losipescu, Arcan and compact shear specimens. These specimens can have complicated stress states with high shear and normal strain gradients. To evaluate the sensitivity of the shear gage to normal strains, shear gages were tested on an Arcan specimen. The Arcan specimen is a notched specimen that can be loaded in pure shear (90 deg), pure tension (0 deg) and at intermediate 15- deg increments. The shear modulus for an aluminum specimen was determined at each of these loading angles. It was found that the gages display nearly zero sensitivity to normal strains ( _x, _y). Moiré interferometry was used to document the shear and normal strain distributions in the test section and to provide an independent method for determining the average shear strain. These results reinforce the robust nature of testing with the shear gage.     

An analysis of ductile rupture modes at a crack tip

An elastic-Viscoplastic model of a ductile, porous solid is used to study the influence of the nucleation and growth of micro-voids in the material near the tip of a crack. Conditions of small scale yielding are assumed, and the numerical analyses of the stress and strain fields are based on finite strain theory, so that crack tip blunting is fully accounted for. An array of large inclusions or inclusion colonies, with a relatively low strength, results in large voids near the crack tip at a rather early stage, whereas small second phase particles in the matrix material between the inclusions require large strains before cavities nucleate. Various distributions of the large inclusions, and various critical strains for nucleation of the small scale voids between the inclusions, are considered. Localization of plastic flow plays an important role in determining the failure path between the crack tip and the nearest larger void, and the path is strongly sensitive to the distribution of the large inclusions. Values of the J-integral and the crack opening displacement at fracture initiation are estimated, together with values of the tearing modulus during crack growth, and these values are related to experimental results.