Steep Stress Gradients Research Articles

Free-edge effects analysis of angle-ply laminates under transverse loading using layer-wise finite-element method with semi-analytical shear stress calculation

Free-edge stress fields are of an utmost localized nature exhibiting steep stress gradients and they rapidly decay with increasing distance from the laminates’ edges. Layer-wise theory has already been used to analyse the stress field at the free edges of the laminates. In this investigation, the layer-wise theory in finite-element method (FEM) is used to analyse the stress field of the laminates’ free edges. In this study, apart from the conventional FEM in which the stresses are calculated from the constitutive laws, the shear stress components along the thickness are calculated from the equilibrium equations by employing a semi-analytical approach. It is shown that the obtained stresses from the current investigation are very close to those available from the three-dimensional elasticity solution for a square laminate under transversely double sinusoidal pressure distribution. To investigate the free edge influence on shear stress distribution of laminates under transverse loading, the analyses are performed for three angle-ply lay-ups with clustered and alternating sequences. It is shown that the free edge effects of angle-ply laminates with different stacking sequences under transverse pressure loading could be considerably different from laminates with in-plane loading conditions.

X-ray analysis of steep residual stress gradients: The 2θ-derivative method

Abstract Machined ceramics and other hard materials exhibit very steep subsurface gradients of residual stresses. X-ray analysis enables the non-destructive assessment of the distributions of these residual stresses versus the distance from the surface via variation of the penetration depth of the X-rays. Conventional evaluation procedures are based on continuous or piecewise defined polynomial functions of stress versus distance, which are fitted to the X-ray data by means of complex solution schemes. These solution schemes are, however, in many cases unstable and difficult to handle. We have developed an entirely novel evaluation procedure which is based on polynomials fitted to the “2θ vs. sin2 ψ” plots obtained from the X-ray measurements. It is shown that the residual stress profiles can be computed explicitly from these polynomials without any further assumptions. The evaluation procedure is described in detail and demonstrated in a case study on ground alumina ceramics.

Measurement of Torsionally Induced Shear Stresses in Shrink-Fit Assemblies

Shear stresses along the shaft/hub interface in shrink-fit components, generated by torsional loads, can drive premature failure through fretting mechanisms. It is difficult to numerically predict these shear stresses, and the associated circumferential slip along the shaft/hub interface, due to uncertainties in frictional behaviour and the presence of steep stress gradients which can cause meshing problems. This paper attempts to provide validation of a numerical modelling methodology, based on finite element analysis, so the procedure may be used with confidence in fitness-for-purpose cases. Very few experimental techniques offer the potential to make measurements of stress and residual stress interior to metallic components. Even fewer techniques provide the possibility of measuring shear stresses. This paper reports the results of neutron diffraction measurements of shear stress and residual shear stress in a bespoke test specimen containing a shrink-fit. One set of measurements was made with a torsional load ‘locked-in’. A second set of measurements was made to determine the residual shear stress when the torsional load had been applied and removed. Overall, measurement results were consistent with numerical models, but the necessity for a small test specimen to allow penetration of the neutron beam to the measurement locations meant the magnitude of shear stresses was at the limits of what could be measured experimentally.

X-ray diffraction at constant penetration depth – a viable approach for characterizing steep residual stress gradients

The experimental analysis of near-surface residual stresses by X-ray diffraction methods is based on measuring the spacings of lattice planes while the inclination ψ with respect to the surface plane is changed stepwise. A characteristic feature of conventional techniques is that the penetration depth of the X-rays is altered as inclination is varied. By simultaneously varying three different goniometer angles in a particular fashion, both the penetration depth and the measuring direction can be held constant while ψ is varied. Thus the normal and shear stresses can be derived from the sin2ψ plots by means of standard evaluation procedures developed for gradient-free stress states. The depth profile of residual stress is then obtainedviaLaplace transformation of the results from several stress measurements carried out at different penetration depths. In the present paper, the feasibility of this experimental approach for characterizing the strongly graded, non-equiaxed stress state existing at a machined surface is demonstrated. The results from constant-penetration-depth measurements on the ground surface of an engineering ceramic are compared with those from conventional sin2ψ measurements.

Prediction of fretting crack propagation based on a short crack methodology

Fretting tests have been conducted to determine the maximum crack extension under partial slip conditions, as a function of the applied tangential force amplitude. An analytical elastic model representing a fretting-induced slant crack has been implemented and combined with the Kitagawa–Takahashi short crack methodology. This approach provides reasonable qualitative agreement between experimental and predicted maximum fretting crack lengths as long as the global response of the interface remains elastic. It confirms the stability of the crack arrest approach to predict the fretting fatigue endurance. It is, however, observed that the model is systematically conservative when significant plastic deformations are generated in the interface. A discussion of the appropriate fundamental parameters when dealing with steep stress gradients such as those present in fretting, and which are difficult to interpret in the context of the Kitagawa–Takahashi method, is presented. It is also shown that the maximum crack length evolution under plain fretting wear test conditions can be used to calibrate fretting fatigue predictions.

A consistent crack modelling and analysis of rectangular hollow section joints

This paper proposes a flexible approach to model one or several cracks under the weld toe of a rectangular hollow section (RHS) joint by mapping the two-dimensional crack's curvature onto the three-dimensional crack surface. Based on this model, an automatic mesh technique is developed to generate the entire finite element mesh of the damaged joint. This method can generate the mesh of cracks with any length, position, quantity, shape, and type (surface crack or through-thickness crack). Because of the steep stress gradient at the stress concentration region, the mesh around the crack front is refined using several mesh refinement steps to capture the stress distribution accurately. The generated model is then applied to study the plastic collapse load and crack opening displacement (COD) of some cracked RHS T-joints. Comparison between the numerical results and experimental test data shows that a good agreement is obtained for a typical RHS T-joint specimen subjected to brace end tension load. Thus, it confirms the efficiency and reliability of the proposed modelling approach for any cracked RHS T-joints.

A micromechanical approach to fatigue in small notches*

ABSTRACTThe present work shows the application to small notches of a micromechanical model which describes the growth of a short crack across the steep stress gradient generated at the root of a notch. The model, based on the theory of distributed dislocations, takes into account the interaction between short cracks and material barriers such as grain boundaries. The term ‘small notches’ refers in this paper to stress raisers the size of which is of the same order as the characteristic microstructural unit of the material. Typical examples are superficial scratches, corrosion pits, inclusions or pores. Comparisons between predicted fatigue limits and experimental results reported in the literature for different materials containing small artificial defects are shown and discussed.

Predicting the fretting fatigue limit for spherical contact

One of the most relevant factors controlling fatigue crack propagation under fretting conditions is the steep stress gradient produced in the material by contact loads, a situation also found in notch problems. This suggests that crack growth can be analysed using methodologies similar to those employed in notched components. In this work, we assess the ability of various methods originally used in notched components to predict fatigue failure in specimens undergoing fretting fatigue with spherical contacts. The effect of the local changes in the stress ratio along the crack path was considered in all cases. The predictions thus obtained are compared with a number of experimental results for Al-7075-T6.

Solution behavior of the falling sphere problem in viscoelastic flows

Thehp-finite element method and pseudo arc-length method are combined to track solution behavior of the steady flow of a sphere falling in a tube filled with viscoelastic fluids. The computations is proved to be convergent and stable by a posteriori error analyses; the solutions smooth and with extremely steep stress gradient are obtained by using appropriate high-order interpolation distributions. The commonly used drag coefficient is proved not a reliable indicator for the approximation error. The solution curves of the upper convected Maxwell (UCM) and the Oldroyd-B fluids clearly indicate that there exist limiting points, parameterized by the Deborah number, where the magnitude of the solutions and the axial normal stress gradients behind the rear stagnation rise up rapidly, maybe go to infinity. The limiting points can be simply removed by employing the modified Chilcott and Rallison (MCR) fluid, which replaces the infinitely extendable, linear Gaussian chain with the finitely extendable nonlinear elastic spring (the FENE chain). Therefore the limiting behavior is caused by the physical model; it is not a numerical artifact.

Effects of tooling on the residual stress distribution in an inertia weld

Neutron diffraction residual strain measurements have been made on a tubular structure formed by joining two nickel-based superalloy RR1000 parts by inertia welding. Residual strains in the radial, hoop and axial directions of the tube cross-section have been measured. The corresponding residual stress field has been calculated accounting for the stress-free lattice parameter variations in the region close to the weld line. Tensile residual stresses were observed near the inner diameter of the tube with magnitudes of the order of +500, +1100 and +1300 MPa in the radial, axial and hoop directions, respectively. By comparison near the outer diameter (OD) of the weld the corresponding stresses are of the order of −200, −1000 and 150 MPa. The final stress state reflects the influence of the gripping fixture tooling and thermal gradients during inertia welding. Additional X-ray (at the surface) and hole-drilling (at the near surface) measurements show a steep residual stress gradient in the near surface region. Tensile hoop and axial machining stresses at the surface indicate the potential for improving the inertia weld tooling and the machining parameters used when removing the flash.

Elasticity Solution for a Laminated Orthotropic Cylindrical Shell Subjected to a Localized Longitudinal Shear Force

A three-dimensional elasticity solution is presented for the title problem. The solution is in terms of a double Fourier series in the surface-parallel directions and a power series in the thickness direction. On the basis of this solution, it is shown that the classical lamination theory is inadequate for this problem because the steep displacement and stress gradients near the load cannot be captured by it correctly even if the shell is thin.

Effects of Taper Variation on Conical Threaded Connections Load Distribution

Threaded connections are used in a lot of mechanical and civil engineering applications and, nowadays, are perhaps the most developed and economical way to join two elements made of any kind of material. It is well known that when a bolt is screwed into a threaded hole, the first threads engaged bear more than half of the axial load induced by the make-up torque. This overload in correspondence with the first threads engaged, together with the steep stress gradient induced by the notch effect at the thread root, is the cause of dramatic fatigue failures. Moreover, it is on the first threads engaged, because of the presence of high contact loads on the flanks of the threads, that galling can arise and promote surface damage if the threaded connection has to be screwed and unscrewed many times. The object of this paper is to propose a numerical finite element procedure, confirmed by means of full-scale experimental tests, which makes it possible to quantify the effects induced by varying the taper of rotary shouldered connections (RSCs), in terms of stress state, loads carried by the threads and pressure on the thread flanks. RSCs are conical threaded connections used in the oil industry and the aim of the procedure is to provide the designer with a useful tool able to minimize the dangerous effects of galling and overload.

Determination of steep stress gradients at surfaces or interfaces by means of neutron diffraction

Abstract A series of measurements has been performed on the neutron strain scanner of the Laboratoire Leon Brillouin in order to explore the limits of the spatial resolution achievable by neutron stress analysis. Two types of samples were investigated, i.e. sandwich structures consisting of thin sheets of copper and aluminum nitride (AIN) and shot peened steel sheets. With slits before and after the sample as small as 0.3 × 10 mm2 (AIN) or even 0.15 × 10mm2 (steel) counting times were not longer than 1–2 h/peak. Checks revealed that a spatial resolution of ≈0.3 mm (AIN) resp. 0.15 mm (steel) was indeed achieved in the direction perpendicular to the surface. Using partial immersion of the gauge volume, near-surface/interface strains could be explored with even higher spatial resolution, down to ≈30 μm in the case of steel. The stress gradients determined by neutron diffraction were checked by measurements using other techniques.

Determination of steep stress gradients by X-ray diffraction — results of a joint investigation

Stresses caused by surface treatments show principally a profile versus the depth beneath the surface. The stress profile may be very steep near the surface, in which case the methods of its determination are restricted to those using X-ray diffraction. Various methods of stress gradient determination are known using layer removal or determining the profile from measurements at the original surface. The evaluation procedures are very susceptive to the accuracy of the measurements, especially when gradients are steep. Recommendations for measurement parameters and for the evaluation of steep stress gradients should be assessed. This was the reason to initiate this joint task to study very steep gradients and to elaborate respective recommendations. Participants came from several universities, research institutes and from industry. Two sets of identically treated specimens were produced and studied at the different institutions. Case hardened and subsequently ground samples of 16MnCr5 steel and ground samples of Si 3N 4 ceramic material were chosen. One special set of lattice-strain distributions has been evaluated by several participants to compare and test the procedures of stress gradient evaluation that are used by the different institutions. Recommendations are given for the procedure of measurement and evaluation to determine steep stress gradients from measurement at the original surface.

A New Approach to Evaluate Steep Stress Gradients Principally Using Layer Removal

A new method is, reported to determine a triaxial residual stress (RS) profile as a function of the distance z from the surface from experimental X-ray data for several penetration depths T without using a Laplace transformation explicitly. The method is based on the fact, that if stress states in a thin layer vary linearly over the depth of the isolated layer, an experimentally determined RS value σ(τ) for a particular τ corresponds to a(z) with z = τ.. The method requires at least two strain-τ-profile measurements at the as-manufactured surface and at each new surface after stepwise removal thin layers using different lattice planes {hkl} or wavelengths λ or the diffractometer both in the Q- or Ψ-mode. In case of a biaxial stress state it is sufficient to measure a single strain-τ-profile in each step.

Ｘ線材料強度 Ｎｉ‐Ｃｏ‐Ｐ／α‐Ｓｉ３Ｎ４複合めっき材のＸ線応力測定 応力勾配を考慮したＮｉ‐Ｃｏ‐Ｐ相の残留応力測定

Ni-Co-P/α-Si3N4 composite plating excels in wear-and corrosion resistance. It is important to evaluate the residual stress due to the misfit of mechanical and physical properties between plating and substrate during the manufacturing and industrial using. However, in the case of plating specimen which have stress gradient, the sin2Ψ method is not adequate to use because this material shows severely curved sin2Ψ diagram.In this study, a fundamental investigation was carried out to apply the X-ray residual stress measurement of the plating material. Fourth kinds of specimens with different thickness of film were prepared. X-ray elastic constants were obtained using the non-liner analysis. Influence of the film thickness on curvature of 2θ-sin2Ψ diagram was simulated. Residual stress in the plating layer was analyzed under the assumption that the stress state is equivalent biaxial.Some experimental results were observed: sin2Ψ diagrams were severely curved, and shape of diagrams shows varied by the film thickness and X-ray penetration depth. There is the steep stress gradient in the direction of depth.As the results, X-ray elastic constants of all specimens were independent from the thickness of film. Therefore, the value is constantly. A value of residual compressive stress calculated form present method is grater than value of sin2Ψ technique. Compressive stress decreased with the film thickness.

The effect of recessing on the stresses in adhesively bonded single-lap joints

An alternative technique of bonding single-lap joints was investigated by removing portions of the adhesive from the interior of the overlap. This technique is termed as recessed bonding. Recessed bonded joints were analyzed using the finite element method. A linear, two-dimensional, plane strain analysis with isotropic materials was conducted. The stress distributions at the adhesive mid-thickness and interface were determined for joints with various levels of recessing, and compared to the stress distributions in continuous single-lap joints. In continuous single-lap joints, maximum stresses occur near the adhesive spew terminus. In recessed single-lap joints, maximum stresses remain near the adhesive spew terminus, and increase only slightly with increased level of recessing. At the recess ends steep stress gradients occur, which should be accounted for.

A COMPARISON OF 3-D SPLINE VARIATIONAL AND FINITE-ELEMENT SOLUTIONS FOR A CROSS-PLY LAMINATE WITH A CIRCULAR HOLE

A comparison of the finite-element method and the spline variational theory is presented for the three-dimensional stress analysis of a rectangular plate with a circular hole under uniaxial tension. Isotropic, orthotropic, and cross-ply laminates are considered. The finite-element (FE) formulation is based on traditional 20-node isoparametric brick elements. The spline variational theory, or spline variational elastic laminate technology (SVELT), employs a variational approach in which displacements and interlaminar tractions are approximated using sets of B-spline functions. For the isotropic plate and the orthotropic plate, both the FE and SVELT models were sufficiently converged such that vanishing stress components, i.e., the zero-traction conditions at the hole boundary, were reported as less than 0.5% of the average applied stress. A cross-ply laminate [02/902]s was selected to study the effects of the hole-edge/ply-interface singularity on the model's performance. Stresses approaching the singularity in a radial direction along the ply interface at 0°, 45°, and 90° from the load axis are reported. In the vicinity of singularities and steep stress gradients, results indicate that SVELT can reduce problem sizes or degrees of freedom (DOF) by as much as a factor of 4 while obtaining results of comparable accuracy.

Effect of Intermediate Layer on Residual Stress Occurred in Hydroxyapatite Coating Implant.

Hydroxyapatite (HAp) is one of the most effective biomaterials used in an artificial bone and a dental designed implant. Since its mechanical reliability and workability are much lower than those of metal, it is often used as a coating material. However, cracking and delamination at the coating interface are induced by the residual stress which occurs in the coating process. In our previous report, the steep stress gradient in the coating layer and the increase in tensile residual stress on the surface of the substrate were obtained using the polychromatic X-ray diffraction. Therefore, an additional intermediate layer between the coating and the substrate material may decrease the residual stress in the coating layer. In this work, we describe the method to measure nondestructively three dimensional residual stress generated in the coating implant with the intermediate layer, using the polychromatic X-ray diffraction. As a result, the compressive residual stress in the coating layer of the hydroxyapatite coating titanium implant with the titania intermediate layer, made by atmospheric plasma-spray processing, was smaller than that of the implant coated only with hydroxyapatite.

Analysis of Stress Gradient in Ceramic Film by X-ray Method.

The sin2 ψ diagram taken from a specimen with steep stress gradients beneath the surface shows nonlinearity, because the X-ray penetration depth changes depending on the tilt angle. Stress gradients can be determined from this nonlinearity. Since ceramic materials have deep X-ray penetration depth, the thickness of a ceramic thin film should have a significant effect on the nonlinearity of the sin2 ψ method. In this paper, we propose a method of X-ray measurement of the stress gradient, which takes into account film thickness under the assumption of linear stress distributions. A 58-μm-thick silicon nitride film was prepared. The film specimen was polished carefully with diamond slurry to obtain sharp profiles of the X-ray diffraction. To obtain a steep stress gradient, the specimen was bent on a cylinder. The stress distribution estimated by the present method agreed well with the applied bending stress. In conclusion, the stress gradient should be analyzed by the weighted average stress on the basis of the intensity of the diffracted X-rays from the entire thin film, when the thickness is six times larger than the effective X-ray penetration depth.