Loading Orientation Angle Research Articles

Measuring elastic parameters of transversely isotropic materials by cylindrical indentation

Based on the cylindrical indentation experiments, a novel model for characterizing the elastic mechanical property of transversely isotropic materials has been established. The cylindrical indentation of transversely isotropic materials was theoretically and dimensionally analyzed. Three-dimensional (3D) indentation experiments that encompass the wide range of transversely isotropic material parameters were simulated by finite element. The effect of each parameter (transversely isotropic Young’s modulus, EP , longitudinal Young’s modulus, EL , longitudinal shear modulus, GL , and loading orientation angle, α) on the normalized indentation modulus was investigated. Then, the dimensionless analytical relationship between indentation moduli and elastic parameters was obtained at three different indentation orientations . Several groups of transversely isotropic materials were selected as input parameters to carry out numerical indentation experiments for the error analysis. The sensitivity of the calculated elastic parameters to the experimental data was analyzed. Simultaneously, the technique was used in the particular case of a Zinc single-crystal material, and the accuracy of these derived formulas was verified. The good agreement shows that the proposed method is reliable and could be applied to characterize the elastic parameters of transversely isotropic materials.

Loading Orientation Effects on the Strength Anisotropy of Additively-Manufactured Ti-6Al-4V Alloys under Dynamic Compression

The microstructure of additively-manufactured metals depends on the direction of build, and is distinctly different from those of conventional metals. This work examines the effect of strain rate, heat treatment, and loading orientation relative to the build direction of Ti-6Al-4V samples that have been additively manufactured by direct metal laser melting to determine how the microstructure affects overall mechanical properties. The effect of rate dependence on additively manufactured Ti-6Al-4V was investigated by compressing cylinders of the material both quasi-statically in a screw-driven load frame (10−4 s−1 to 10−1 s−1), and dynamically in a split Hopkinson (Kolsky) pressure bar system (375 s−1 to 6000 s−1). The yield strength of the additively manufactured Ti-6Al-4V was observed to monotonically increase with increasing strain rates and the samples failed along a 45° direction through the thickness regardless of loading orientation. As in the case of traditionally forged metals, annealed additively manufactured Ti-6Al-4V samples exhibited lower yield strengths than their non-annealed counterparts at similar strain rates. For quasi-static loads, a clear dependence of response on loading orientation angle with respect to the material layering direction was seen, with the yield strength being greatest when loading was applied parallel to the build direction – a notable contrast to what is observed in tensile results in which the yield strength is lowest when tension is applied along the build direction. No clear relationship between the yield strength and loading orientation was observed in the dynamic tests, likely because the differences were within the measurement uncertainty of the method.

Analytical stress solution for an infinite plate containing two oval holes

Abstract The problem refers to an elastic infinite plate bounded by two oval holes, which is subjected to uniform surface tractions on the boundary of the holes and uniform tension and shear stress at infinity. By looking for a new mapping function, the considered region is conformally mapped onto an annulus, and a complex variable method is used to obtain the stress solution. The problem that an elastic infinite plate contains two circular holes or a circular hole and an oval hole is the special case of this article. The present solution has been validated by both published solutions for special cases and ANSYS software. Some computational examples are given to investigate the effects of the separation distance of the two holes, relative ratio of applied stresses, surface tractions on the boundaries, the size of a hole, shear stress at infinity and the loading orientation angle on the stress distribution of the hole boundaries. Practical significance of the solution is placed in the fact that it could be used as a quick-solver with high accuracy.

Characterizing the mechanical behaviour of the Tournemire argillite

Abstract A laboratory programme of uniaxial, triaxial, cyclic and Brazilian tests was conducted to investigate the anisotropic mechanical behaviour of the Tournemire argillite, with different axial loading orientations with respect to the bedding planes (i.e. loading orientation angle, θ=0°, 30°, 45°, 60° and 90°). The experimental results show that both strength and deformation of the argillite are direction-dependent. Failure occurs in a brittle manner with a sudden collapse of the material strength. The failure mode exhibits localization along distinct failure planes and also depends on the loading orientation. This paper summarizes the experimental results and describes constitutive relationships that were developed in order to simulate the stress–strain behaviour of the Tournemire argillite. A microstructure tensor approach is adopted in order to take into account the anisotropic behaviour of the argillite. The identification procedure for material function and parameters is outlined, and the model is applied to simulate the set of triaxial tests performed at different levels of confining pressure and orientation of the bedding planes. It is demonstrated that the model adequately reproduces the anisotropy, the pre-peak stress–strain response and the onset of material collapse in those tests.

Estimation of Mixed-Mode Stress Intensity Factors with Presence of the Confinement Parameters T-Stress and A3

A failure criterion is proposed for ductile fracture in U-notched components under mixed mode static loading. The Compact Tension Shear (CTS) is the preferred test specimen used to determine stress intensity factor in the mode I, mode II and the mixed-mode fracture. In this work, the mode I and mode II stress intensity factors were computed for different notch ratio lengths 0.1<a/W<0.7, of the inner radius of notch 0.25mm<ρ<4mm and load orientation angles 0°<α< 90° using finite element analysis. However, a review of numerical analysis results reveals that the conventional fracture criteria with only stress intensity factors (NSIFs) Kρ first term of Williams’s solution provide different description of stress field around notch zone comparing with results introduce the second and third parameter T-stress and A3.

On the Parameter Identification of Polynomial Anisotropic Yield Functions

Nonquadratic anisotropic yield functions have been developed in recent years for many lightweight automotive sheet metals. Realization of the improved performance of these advanced anisotropic yield functions depends in part on a careful calibration of their material constants via simple mechanical tests. This paper describes a novel approach on the parameter identification of plane–stress polynomial anisotropic yield functions by recasting them in a special form in terms of two principal stresses and one loading orientation angle. Independent mechanical tests for the parameter identification can thus be classified according to the plane stress state and the in-plane loading orientation, respectively. Parameter identification options have been examined in detail for a fourth-order homogeneous polynomial anisotropic yield function using the proposed approach. Some new insights have been gained on the permissible types and the number of independent mechanical test measurements per type that are needed for fully calibrating the material constants of the fourth-order yield function. The use of equal biaxial plastic strain ratio instead of equal biaxial yield stress makes the experimental calibration of the yield function more feasible as only simple in-plane uniaxial tension and out-of-plane compression tests of sheet metal samples are required.

Laboratory investigation on the mechanical behaviour of Tournemire argillite

This paper presents the results of a laboratory testing program that was designed to investigate the mechanical behaviour of the Tournemire argillite. Eighty rock samples were obtained from boreholes drilled at different angles in the walls and floor of an existing gallery at the Tournemire Underground Research Laboratory (URL), France. The experimental program consists of the measurement of the physical properties of the argillite and its mechanical response to loading during uniaxial tests, triaxial tests with various confining pressures, unconfined and confined cyclic tests, and Brazilian tests. Since the Tournemire argillite is characterized by the presence of closely spaced bedding planes, the rock specimens were loaded in different directions to bedding planes (i.e., loading orientation angle, θ = 0°, 30°, 45°, 60°, and 90°). Acoustic emission data were also recorded to detect the initiation and propagation of micro-cracks during the uniaxial tests. Most of the tests were performed at the natural moisture content of the rock specimens as delivered to CANMET Laboratories in Ottawa, Canada, where the experiments were conducted. The main objective of the testing program is to identify the mechanical properties of the Tournemire argillite. This paper mainly focuses on the description and interpretation of the test results. The development of an elastoplastic-damage model to describe the mechanical behaviour of the Tournemire argillite is the subject of another paper.

Path-independent integrals around two circular holes in an infinite plate under biaxial loading conditions

An analytic solution is presented for stresses induced in an infinite plate with two unequal circular holes by remote uniform loadings and arbitrary internal pressures in the holes. The solution is obtained by using the general expression for a biharmonic function in bipolar coordinates. The Airy stress function is decomposed in the sum of a fundamental stress function for an infinite plate remotely loaded, which gives non vanishing tractions on the circular boundaries, and an auxiliary stress function required to satisfy the boundary conditions on the pressures at the edges of the holes, which produces vanishing stresses at infinity. Correspondingly, the variations of the stress concentration factor are determined in terms of the holes geometry and loading conditions. The path independent J k - ( k = 1, 2), M- and L-integrals are analytically calculated on a closed contour encircling the two holes, under remote loading, in order to evaluate the energy release rates accompanying unit translation, self similar expansion and rotation of the holes, respectively. Results are then presented for varying loading orientation angle, biaxial loading ratio and holes geometry.

Experimental and Numerical Investigation of the Mixed-Mode Delamination of PAN Based Carbon/Epoxy Composite Using Modified Arcan Fixture

The present research examines analytically and experimentally the mode-I and mode-II and mixed mode-Interlaminar fracture toughness of PAN based carbon/epoxy composite. A modified Arcan fixture, well-suited for the study of the behavior of used composite assemblies, was developed in order to focus on the analysis of the fracture behavior of the material. The edge effects are minimized by using an appropriate design of the substrates so that experimental results give reliable data. Also the mode-I and mode-II stress intensity factors were computed for different crack lengths and load orientation angles using finite element analysis. The numerical results show that the modified Arcan specimen is able to provide pure mode-I, pure mode-II and any mixed mode loading conditions. It is shown that the results obtained from the fracture tests are consistent very well with mixed mode fracture theories. Obtained results indicated that fracture toughness and stress intensity factor for sliding mode enhanced up when the loading angle increased. Mechanism of fracture and toughening were examined by using scanning electron microscopy.

A planar plastic flow theory of orthotropic sheet metals and the experimental procedure for its evaluations

Abstract An anisotropic plasticity theory is formulated for describing planar flow behaviours of orthotropic polycrystalline sheet metals. Flow rules are derived for both the macroscopic plastic rate of deformation tensor and the macroscopic plastic spin tensor by considering a small set of activated macroscopic slips or shearing modes in a sheet metal. An internal state variable other than the effective plastic strain or equivalent plastic work is introduced to define the isotropic hardening state of the sheet metal so that effects of anisotropy of a sheet metal on its isotropic hardening behaviour can be better taken into account. The theory requires a total of five anisotropic material functions of a loading orientation angle, an effective rate-dependent stress–strain curve and a stress exponent to describe the planar anisotropic plastic flow behaviour of the sheet metal. The five anisotropic material functions are specified based on the orthotropic symmetry of the sheet metal and each of them may be expressed as a Fourier sine or cosine series. The experimental strategy and procedure for direct determination of the material constants in the theory by simple mechanical tests are discussed in great details. In particular, a special case of the proposed flow rules of macroscopic plastic rate of deformation tensor and macroscopic plastic spin is considered and it is found that it can describe satisfactorily the experimental data on both the directional dependence of plastic strain ratio and yield stress as well as the rotation of the material symmetry axes of an orthotropic steel sheet subjected to off-axis uniaxial tension.

Modeling the Rotation of Orthotropic Axes of Sheet Metals Subjected to Off-Axis Uniaxial Tension

A simplified version of a newly developed anisotropic plasticity theory is presented to describe the anisotropic flow behavior of orthotropic polycrystalline sheet metals under uniaxial tension. The theory is formulated in terms of the intrinsic variables of principal stresses and a loading orientation angle and its uniaxial tension version requires a non-quadratic stress exponent and up to five anisotropic material functions of the loading orientation angle to specify a flow condition, a flow rule for plastic strain rates, a flow rule for macroscopic plastic spin, and an evolution law of isotropic hardening. In this investigation, the proper analytical form and the associated parameter identification of the anisotropic material functions defining the flow rule of macroscopic plastic spin are discussed for sheet metals with persistent but rotated orthotropic symmetry axes under off-axis uniaxial tension. It is shown that the proposed flow rule of macroscopic plastic spin can successfully model the experimental data on the rotation of orthotropic symmetry axes in the three sheet metals reported, respectively, by Boehler et al. (Boehler and Koss, 1991, Advances in Continuum Mechanics, O. Bruller et al., eds., Springer, Heidelberg, pp. 143–158; Losilla, Boehler, and Zheng, 2000, Acta Mech. 144, pp. 169–183); Kim and Yin (1997, J. Mech. Phys. Solids 45, pp. 841–851); and Bunge and Nielsen (1997 Int. J. Plasticity 13, pp. 435–446).

Control of Rotation and Swing of a Rigid Body Suspended Load Using Inertia Rotors.

This paper describes rotational control and swing suppression of a crane suspended load model. A rotational free rigid body suspended by a single rope is controlled using three inertia rotors. Fiber optical gyros installed on the suspended load are used to measure the load orientation angles. Controlling angles and angular velocities are obtained from measured data using the conversion between zxy and zxz Euler angles and the driving system of the inertia rotors are developed based on the coupling dynamics. Experiments and simulations show that the rotational orientation is controlled without problems, but swing control is possible under some limit conditions of the load mass size and the rope length, since the gravity force act on the swing motion.