Micro-Raman analysis of stress in machined silicon and germanium

Residual strain in single point diamond machined crystalline silicon and germanium has been measured with high spatial resolution (≈ 2 μm) using Raman microprobe spectroscopy. Raman spectroscopy is a direct, non-destructive technique which provides a spatial resolution down to the excitation wavelength and which may be applied to a wide range of non-conducting materials. Raman scattering was used to measure local strain at various points across single point plunge and feed cuts in crystalline silicon and germanium. Spectra were obtained using various excitation wavelengths (514.5 and 488.0 nm), which, due to their differing penetration lengths in the various materials, can provide depth profiles of the residual stress down to approximately 1 μm. In single point plunge cuts little evidence of surface damage was seen and the residual stresses are compressive. Using a 514.5 nm excitation wavelength, we measure a compressive stress of 250 MPa (2.5 kbar) near the outer edge of a single point plunge cut in silicon. At this wavelength, the penetration depth of the laser is 1.0 × 10⁻⁴ cm. This compressive stress was observed to increase to 600 MPa (6.0 kbar) at a depth of 0.6 × 10⁻⁴ cm which was measured using a 488.0 nm excitation wavelength. In single point feed cuts, regions of heavy fracturing were observed as well as regions of little visible damage. In damaged areas tensile stresses of 200–300 MPa (2.0–3.0 kbar) were measured in silicon while in germanium the tensile stress in such regions is 50–100 MPa (0.5–1.0 kbar). In undamaged areas the stresses are compressive with measured values of 50 and 30 MPa (0.5 and 0.3 kbar) for silicon and germanium respectively.     

An elastic–plastic stress analysis steel-reinforced thermoplastic composite cantilever beam

In the present study an analytical elastic–plastic stress analysis is carried out for a low-density homogeneous polyethylene thermoplastic cantilever beam reinforced by steel fibers. The beam is loaded by a constant single force at its free end. The expansion of the region and the residual stress component of σ_x are determined for 0°, 30°, 45°, 60° and 90° orientation angles. Yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. However, it starts first at the upper surface for 30° and 45° orientation angles. The elastic–plastic analysis is carried out for both the plastic region which spreads only at the upper surface and the plastic region which spreads at the upper and lower surfaces together. The residual stress components of σ_x and τ_xy are also determined. The intensity of the residual stress component is maximum at the upper and lower surfaces of the beam, but the residual stress component of τ_xy is maximum on or around the x-axis. The beam can be strengthened by using the residual stresses. The distance between the plastically collapsed point and the free end is calculated for the same load in the beam for 0°, 30°, 45°, 60° and 90° orientation angles.     

Finite element analysis of the rake angle effects in orthogonal metal cutting

The plane-strain finite element method is developed and applied to model the orthogonal metal cutting of annealed low carbon steel with continuous chip formation. Four sets of simulation results for cutting with −2°, 0°, 5°, and 15° rake angle are summarized and compared to analyze the effects of rake angle in the cutting processes. The initial and deformed finite element meshes, as the cutting reaches steady-state condition, are first presented. Simulation results of the cutting forces and residual stresses, along with the X-ray diffraction measurements of the residual stresses generated using a worn cutting tool with 5° rake angle, are used to identify the influences of the rake angle and tool sharpness. Elements are selected to represent three sections along the shear and contact zones and under the cut surface. The normal and shear stresses, distributions of parameters along these three sections, and contours of temperature, plastic strain, and effective stress are then presented. Limitations of the finite element method for metal cutting simulation are discussed.     

A fracture mechanics life prediction methodology applied to dovetail fretting

This work evaluates a fracture mechanics based crack growth life prediction methodology for dovetail fretting fatigue laboratory experiments. The Ti–6Al–4V specimens were configured with angles of 35°, 45° and 55°. Experiments were conducted with constant amplitude loading at R of 0.1 and 0.5 with lives ranging from 100,000 to 10 million cycles. The approach included the contact loads and bulk stress calculated from the finite element method as inputs to the stress and life analysis. Contact stresses were calculated using the contact stress analysis software CAPRI. These stresses were input into a stress intensity factor calculation at the edge of contact. Crack propagation life was calculated from an assumed initial crack size. Analysis showed that propagation consumes a majority of the total life and is insensitive to a large range of initial crack sizes.     

Interlaminar stresses of a rectangular laminated plate with simply supported edges subject to free vibration

The interlaminar stresses in a laminated rectangular orthotropic plate with four sides simply supported edges during free vibration was determined by using the integration method involving the dynamic inertia terms and displacements. The approximate stresses solutions are obtained under the effect of frequencies of vibration for four-layer symmetric cross-ply laminates with the ply configurations [0°/90°]_s and [90°/0°]_s, angle-ply laminates with the ply configuration [45°/−45°]_s. Numerical results show that the natural frequency has significant effects on the dominant interlaminar stresses in the stacking sequences [0°/90°]_s, [90°/0°]_s and [45°/−45°]_s.     

Erosive wear by silica sand on AISI H13 and 4140 steels

The erosive wear behaviour of AISI H13 tool steel and AISI 4140 steel has been investigated in this work using a sand blast-type rig. Samples of six different hardness levels (from annealed to 595 HV) were produced and subsequently tested using silica sand as the erodent material at impact angles ranging from 10° to 90°, air drag pressures of 0.689 and 1.38 bar (10 and 20 psi respectively), impact speeds ranging from 70 to 107 m s⁻¹ and various particle sizes. Results of erosion versus impact angle at different hardness levels showed three distinctive wear regions: (i) for impact angles of 10° and 20°, the amount of wear was higher at lower hardness values; (ii) for impact angles of 30° and 40° no significant changes were found in the amount of wear despite the increase in hardness; (iii) for impact angles of 60°, 75° and 90° the amount of wear was higher for higher hardness levels in the eroded material. Single curves showed typical ductile behaviour of these alloys, a transition towards brittle behaviour for the hardest specimens was also observed due to the formation of adiabatic shear bands. SEM analysis was conducted to identify the erosion mechanisms for each type of behaviour.     

A method for achieving effective load transfer between the inner and outer layers of a two-layer braided high-pressure hydraulic hose

A method is proposed for accommodating the misfit between two layers of a braided hose. This is achieved by laying the inner and outer braids at angles that lie symmetrically on either side of the equilibrium helix angle of tan⁻¹ 2 for a single-layer hose. The theory of the method is developed and it is shown that a difference of helix angles of 4° or more will accommodate the fractional radial misfit of 3 × 10⁻³ existing in a particular sample of hose. An analysis of the wire tensions in a pressurised hose, assuming constant inter-layer volume, revealed that seriously unequal tensions exist in the two layers if the two helix angles lie asymmetrically about tan⁻¹ 2. The process of taking up misfit, now proposed, generates asymmetry. However this asymmetry and the associated inequality of wire tension decreases as the difference of braid angles increases. Guided by this generalisation, it is demonstrated that an acceptable hose design is achieved if the inner braid is laid at an angle of 59·74° and the outer braid at 49·74°. The geometrical changes that take up the misfit at low pressures produce an extension of the hose of 0·65% and reduce the braid angles by about . The ratio of final tensions in the two layers is 0·93. The analysis in the paper leads to the conclusion that manufacturing uncertainties in the angle at which a braid is laid can generate serious inequalities of wire tension. In the specific illustrative example analysed here an uncertainty of ±1° in braid angle will cause the ratio of wire tensions to vary, but it never falls below a value of 0·63.     

Solid particle erosion of CFRP composite with different laminate orientations

The solid particle erosion behavior of epoxy base unidirectional and multidirectional carbon fiber reinforced plastic composites was investigated. The erosion rates of these composites were evaluated at various impingement angles (15–90°) with a particle velocity of 70 m/s. Irregular SiC particles with an average diameter of 80 μm was used. The dependence of impingement angle on the erosive wear resembled the conventional ductile behavior with maximum erosion rate at 15–30° impingement angle. The erosion rate of unidirectional composites at acute impingement angle was higher for [90] than for [45] and [0] while the difference disappeared at normal impingement angle (90°). On the other hand, the erosion rates of multidirectional laminated composites ([0/90], [45/−45], [90/30/−30] and [0/60/−60]) were not much influenced by the fiber orientation except for 15° impingement angle.     

Effects of Cutting Angles in Ti-6al-4v Milling Process on Surface Integrity: Influence of Roughness and Residual Stresses on Fatigue Limit

□ The influence of the milling process on the fatigue behavior of a titanium alloy was investigated. The effect of cutting conditions such as the cutting angles (axial and radial rake angle) on the surface integrity (roughness and the residual stresses) was observed. The results indicated that the cutting angles have a limited influence on roughness parameters, whereas the effects on residual stresses were greater. A negative axial rake angle induced compressive residual stresses regardless of the radial rake angle. In contrast, a positive axial rake angle combined with negative radial rake angle induced tensile residual stresses. To evaluate the fatigue limit, the four point fatigue tests were carried out. Result showed the fatigue limit is sensitive to the surface integrity. The fatigue limit was also evaluated by analytical method (Arola model). A good correlation was found between the analytical results and the experimental results when cutting angles induced compressive residual stress. However the Arola model was less accurate for tensile residual stress surface condition. To improve the prediction precision, the residual stress was considered as a sensitivity parameter and added to Arola model.     

On the effect of crystallographic orientation on ductile material removal in silicon

In this work the critical chip thickness for ductile regime machining of monocrystalline, electronic-grade silicon is measured as a function of crystallographic orientation on the (0 0 1) cubic face. A single-point diamond flycutting setup allows sub-micrometer, non-overlapping cuts in any direction while minimizing tool track length and sensitivity to workpiece flatness. Cutting tests are performed using chemically faceted, −45° rake angle diamond tools at cutting speeds of 1400 and 5600 mm/s. Inspection of the machined silicon workpiece using optical microscopy allows calculation of the critical chip thickness as a function of crystallographic orientation for different cutting conditions and workpiece orientations. Results show that the critical chip thickness in silicon for ductile material removal reaches a maximum of 120 nm in the [1 0 0] direction and a minimum of 40 nm in the [1 1 0] direction. These results agree with the more qualitative results of many previous efforts.     

Investigation of the direction of chip motion in diamond turning

Management of the chips generated in diamond turning is often critical since contact between chips and the workpiece can result in superficial damage to the finished surface. Controlling chip motion is not a trivial process as the proper positioning of an oil or an air stream requires an understanding of the dynamics of a diamond turned chip and the machining parameters that affect it. Previous work [1] introduced the chip curvature parameter, χ, which is useful in predicting chip radius of curvature over a wide range of cutting speeds, depths of cut, tool geometries and workpiece material properties. To control chip motion, however, an understanding of the direction chips leave the tool/workpiece interface must also be obtained. Cutting experiments were performed investigating the influence of cutting speed, depth of cut, feed rate, tool path angle, tool geometry and tool orientation on the directional characteristics of the motion of diamond turned chips. Flow angle measurements obtained during cutting were found to remain within ± 10° of predictions from a simple geometrical model originally proposed for conventional machining.     

Finite element optimization of diamond tool geometry and cutting-process parameters based on surface residual stresses

In this paper, a coupled thermo-mechanical plane-strain large-deformation orthogonal cutting FE model is proposed on the basis of updated Lagrangian formulation to simulate diamond turning. In order to consider the effects of a diamond cutting tool’s edge radius, rezoning technology is integrated into this FE based model. The flow stress of the workpiece is modeled as a function of strain, strain rate, and temperature, so as to reflect its dynamic changes in physical properties. In this way, the influences of cutting-edge radius, rake angle, clearance angle, depth of cut, and cutting velocity on the residual stresses of machined surface are analyzed by FE simulation. The simulated results indicate that a rake angle of about 10° and a clearance angle of 6° are the optimal geometry for a diamond tool to machine ductile materials. Also, the smaller the cutting edge radius is, the less the residual stresses become. However, a great value can be selected for cutting velocity. For depth of cut, the ‘size effect’ will be dependent upon it. Residual stresses will be reduced with the decrement of depth of cut, but when the depth of cut is smaller than the critical depth of cut (i.e., about 0.5 μm according to this work) residual stresses will decrease accordingly.     

Fatigue behaviour of a commercial zinc-aluminium eutectoid alloy

Constant-amplitude, flexural-fatigue tests have been carried out over the frequency range 8–100 Hz and the temperature range 293–373°K on a commercial zinc-aluminium alloy of basically eutectoid composition. This alloy is highly superplastic at 530°K, when the strain-rate sensitivity of the flow stress index, m, 0·5. At 293°K some residual superplasticity exists and this manifests itself as a frequency effect in the fatigue behaviour. This effect is almost certainly the result of room-temperature, strainrate sensitivity; it is shown by the fact that when the superplastic microstructure is destroyed, the frequency effect disappears. Finally, it is shown that the model proposed by Morrow successfully predicts the fatigue life of this alloy.     

The effects of radial stresses on the strength of thin-walled filament wound GRP composite pressure cylinders

Filament wound glass fibre reinforced epoxy cylinders with thickness : internal diameter ratios of approximately 0.01, and winding angle ± 85° have been tested to failure under different combinations of axial load and internal pressure. The effect of the interaction coefficients in the Tsai—Wu failure criterion equation are considered. Results for the 17 specimens tested and published results for other winding angles have been used to assess some commonly used forms of failure criteria. It was shown that inclusion of the radial stress terms had no significant effect on the experimental results considered. The geometries and hoop to axial stress ratios for which radial stresses are likely to be important are stated.     

Residual stresses in TiN, DLC and MoS2 coated surfaces with regard to their tribological fracture behaviour

Thin hard coatings on components and tools are used increasingly due to the rapid development in deposition techniques, tribological performance and application skills. The residual stresses in a coated surface are crucial for its tribological performance. Compressive residual stresses in PVD deposited TiN and DLC coatings were measured to be in the range of 0.03-4 GPa on steel substrate and 0.1-1.3 GPa on silicon. MoS₂ coatings had tensional stresses in the range of 0.8-1.3 on steel and 0.16 GPa compressive stresses on silicon. The fracture pattern of coatings deposited on steel substrate were analysed both in bend testing and scratch testing. A micro-scale finite element method (FEM) modelling and stress simulation of a 2 μm TiN-coated steel surface was carried out and showed a reduction of the generated tensile buckling stresses in front of the sliding tip when compressive residual stresses of 1 GPa were included in the model. However, this reduction is not similarly observed in the scratch groove behind the tip, possibly due to sliding contact-induced stress relaxation. Scratch and bending tests allowed calculation of the fracture toughness of the three coated surfaces, based on both empirical crack pattern observations and FEM stress calculation, which resulted in highest values for TiN coating followed by MoS₂ and DLC coatings, being K_C = 4-11, about 2, and 1-2 MPa m^1/2, respectively. Higher compressive residual stresses in the coating and higher elastic modulus of the coating correlated to increased fracture toughness of the coated surface.     

Onset of matrix cracking in angle-ply ceramic matrix composites

The problem of initial damage in angle-ply [−θ_m/0_n/θ_m] and [−θ/θ] ceramic matrix composites subjected to axial tension is considered in this paper. The damage is in the form of matrix cracks that may appear in either inclined (−θ and θ lamination angle) or longitudinal layers. As follows from the analysis, if the lamination angle of the inclined layers is small, the initial failure occurs in the 0-layers of [−θ_m/0_n/θ_m] composites or in [−θ/θ] composites in the form of bridging cracks. However, if the inclined layers form a larger angle with the load direction, they fail due to tunneling cracks. It is shown that the boundary between two different modes of failure in a representative SiC/CAS composite corresponds to a lamination angle equal to 35° in the case of [−θ_m/0_n/θ_m] composites. In the case of [−θ/θ] laminates, the boundary value of the lamination angle is equal to 45°, i.e. bridging cracks form if θ<45° and tunneling cracks appear if θ>45°.     

A two-level optimization procedure for material characterization of composites using two symmetric angle-ply beams

A two-level optimization procedure for determining elastic constants E₁, E₂, G₁₂, and ν₁₂ of laminated composite materials using measured axial and lateral strains of two symmetric angle-ply beams with different fiber angles subjected to three-point-bending testing is presented. In the first-level optimization process, the theoretically and experimentally predicted axial and lateral strains of a [(45°/−45°)₆]_s beam are used to construct the strain discrepancy function which is a measure of the sum of the squared differences between the experimental and theoretical predictions of the axial and lateral strains. The identification of the material constants is then formulated as a constrained minimization problem in which the best estimates of shear modulus and Poisson's ratio of the beam are determined to make the strain discrepancy function a global minimum. In the second-level optimization process, shear modulus and Poisson's ratio determined in the first level of optimization are kept constant and Young's moduli of the second angle-ply beam with fiber angles different from 45° are identified by minimizing the strain discrepancy function established at this level of optimization. The suitability of the proposed procedure for material characterization of composite materials has been demonstrated by means of a number of examples.     

Force, torque and plastic flow analysis in rotary upsetting of ring shaped billets

The orbital upsetting of rings has been analysed for a Mises material by using an upper bound approach. Forging forces, rocking die torques and ring profiles are calculated at each step of the process. Experiments are described in which rings made of 1045 mild steel, 52100 chromium alloyed steel and 316 stainless steel are upset at room temperature on a 1.6 MN rotary press. The main parameters are: orbital oscillation angle, 2°, upper die oscillations, 200 min⁻¹ and lower die speed, 4.10 mm s⁻¹. An experimental rocking die placed on a conventional testing machine has been used for the rotary upsetting of rings made of Plasticine as model material. The simulation parameters are: oscillation, 2°, upper die oscillations, 40 min⁻¹, speed, 98.4 mm min⁻¹. The theoretical values of forging forces, rocking torques, and ring profiles are in keeping with the experiments. So the proposed upper bound approach may be considered as a good model for rotary upsetting.     

Autofrettage of thick-walled pipe bends

The bending of a thick-walled cylinder to a given radius involves an elastic–plastic deformation that results in a residual, axial stress distribution. The latter alternates from maximum tension to maximum compression between top and bottom halves of the cross-section. The residual stress levels depend upon the depth of plastic penetration and may be determined as a closed solution when they arise from a bending moment applied to either a non-hardening or linearly-hardening material. When the bent pipe receives an autofrettage treatment without an intermediate heat treatment, this produces a further residual, triaxial stress state. The interaction between the residual states from bending and autofrettage has an important effect upon the net axial stress and the equivalent stress. It is shown that large plastic penetrations arising from bending and autofrettage can residually stress the section beyond its yield point: in tension and in compression across both its halves. With the unloading from each process, a Bauschinger effect reduces the yield point to assist with the onset of reversed plasticity. The latter is far less beneficial than when unloading is elastic. It is shown how a nonlinear kinematic hardening model can be employed to avoid unloading plasticity at the inner and outer diameters. The consequence of interacting residual stresses is that axial stress can play as important a role as hoop stress when designing for safe service loadings. In general, an enhanced residual stress state is beneficial when compressive but detrimental when tensile. Pre-compression is often employed in practice to reduce tensile stress arising from internal pressure, axial force and self-weight. Here, the compressive residuals arising from an autofrettage treatment have long been exploited to enhance the fatigue life of process piping and weaponry.     

Studies of high temperature sliding wear of metallic dissimilar interfaces II: Incoloy MA956 versus Stellite 6

The development of wear surfaces formed during limited debris retention sliding wear of Incoloy MA956 against Stellite 6 between room temperature and 750 °C, and sliding speeds of 0.314 and 0.905 m s⁻¹ (7 N applied load, 4522 m sliding distance) were investigated. At 0.314 m s⁻¹, mild oxidational wear was observed at all temperatures, due to oxidation of Stellite 6-sourced debris and transfer to the Incoloy MA956; this debris separated the Incoloy MA956 and Stellite 6 wear surfaces. Between room temperature and 450 °C, the debris mainly took the form of loose particles with limited compaction, whilst between 510 °C and 750 °C the debris were compacted and sintered together to form a Co–Cr-based, wear protective ‘glaze’ layer. The behaviour was identical to that previously observed on sliding Nimonic 80A versus Stellite 6 at 0.314 m s⁻¹.At 0.905 m s⁻¹, mild oxidational wear was only observed at room temperature and 270 °C and dominated by Incoloy MA956-sourced debris. At 390 and 450 °C, the absence of oxide debris allowed ‘metal-to-metal’ contact and resulted in intermediate temperature severe wear; losses in the form of ejected metallic debris were almost entirely Incoloy MA956-sourced. This severe wear regime was also observed from 510 up to 630 °C, but increasingly restricted to the early stages of wear by development of a wear protective Incoloy MA956-sourced ‘glaze’ layer. This ‘glaze’ layer formed so rapidly at 690 °C and 750 °C, that severe wear was all but eliminated and wear levels were kept low.The behaviour observed for Incoloy MA956 versus Stellite 6 at 0.905 m s⁻¹ contrasts sharply with that previously observed for Nimonic 80A versus Stellite 6, in that the Incoloy MA956-sourced high Fe–Cr debris formed a protective oxide ‘glaze’, whilst the Nimonic 80A-sourced Ni and Cr oxides formed an abrasive oxide that at high sliding speeds assisted wear. The data indicates that the tendency of oxide to form a ‘glaze’ is readily influenced by the chemistry of the oxides generated.