Experimental technique for measurement of stress-acoustic coefficients of Rayleigh waves

Two stress-acoustic coefficients,K ₁ andK ₂, are required to determine the state of biaxial surface stress from ultrasonic Rayleigh-wave velocity or time of flight measurements in elastic, initially isotropic solids. An experimental technique is described for the precise measurement of these two coefficients in uniaxially stressed test specimens. The technique is applied to aluminum 2024-T351 and 6061-T651 alloys. The influence on measurement results of various parameters such as material anisotropy and temperature is considered.     

Residual stress analysis near a cold expanded hole in a textured alclad sheet using X-ray diffraction

In this paper we present the methods of determination and the stress obtained at the periphery of a cold expanded hole in a 2024-T3 Alclad aluminum alloy sheet. The measurements in the aluminum clad were performed by the sin²Ψ method, taking experimental precautions to deal with the texture effects. In the core aluminum a special method had to be implemented to determine the stress values in a direction not accessible to the X-ray diffraction. The strains were measured in sample orientations selected according to the texture characteristics and stress factorsF _ij were used to calculate the stress tensor. TheF _ij values were determined assuming a quasi-isotropic material behavior, after concluding that the stress results were not significantly affected by factors calculated for textured material. The residual stress profile, both in the clad and in the sheet, shows a nearly axisymmetric stress state. Compressive stresses were observed near the periphery of the hole, with values that are higher on the exit than on the entrance face. Residual stresses were also higher in the hoop direction than in the radial direction. They decreased with the radial distance to the hole and affected the previous stress state over a distance of 6 mm. The plastic deformation induced by the cold expansion is well evidenced by the FWHM values, which in the affected zone decrease with increasing distance from the hole edge.     

Elastic–plastic analysis of two-dimensional functionally graded materials under thermal loading

The two-dimensional functionally graded materials, (2D-FGMs) have been recently introduced in order to significantly reduce the thermal stresses in machine elements that subjected to sever thermal loading. To the author’s knowledge no work was found that investigates the elastic–plastic stress analysis for 2D-FGMs. In the current work, a 3D finite element model of 2D-FGM plates made of ZrO₂, 6061-T6 and Ti-6Al-4V with temperature dependent material properties has been proposed to perform such analysis. An elastic plastic stress–strain relation based on the rule of mixture of the 2D-FGM has been introduced in the model. Also, a 3D finite element model of conventional FGM plates, of ZrO₂/Ti-6Al-4V and ZrO₂/6061-T6, with temperature dependent material properties has been proposed for the investigation of these plates too. Then, elastic–plastic stress analysis of the considered four plates (two conventional FGMs and two 2D-FGMs) under the same transient cyclic heating and cooling was carried out. It was found that heat conductivity of the metallic constituents of FGM has great effect on the temperature distributions that resulting from the thermal loads. Minimum temperatures variation and minimum stresses can be obtained using ZrO₂/6061-T6/Ti-6Al-4V 2D-FGM. Also, the results indicate that only ZrO₂/6061-T6/Ti-6Al-4V 2D-FGM can stand with the adopted sever thermal loading without fracture or plastic deformations.     

A simple model for dislocation behavior,strain and strain rate hardening evolution in deforming aluminum alloys

In this work, modeling of the stress–strain behavior is carried out using a simple dislocation model. This model uses three variables to characterize the dislocation population: The average forest and mobile dislocation densities, ρ_f and ρ_m, and the average dislocation mean free path L. However, it is shown that within reasonable assumptions, only two of these variables are independent. The mathematical form derived from this dislocation-based model was applied to experimental stress–strain data determined at room temperature for pure aluminum, 3003-O, 2008-T4, 6022-T4, 5182-O and 5032-T4 aluminum alloy sheets. The evolution of the state variables was calculated for these materials from a single stress–strain curve. The average dislocation mean free paths at a strain of 0.5 were compared with TEM observations of dislocation cell sizes or inter-dislocation spacing for specimens deformed equal biaxially with the hydraulic bulge test. A very good agreement was obtained between predictions and experiments.     

J resistance curves in aluminum SEN specimens using Moiré interferometry

TheU _y -displacement field obtained by white-light moiré interferometry were used to estimate the approximate far- and near-fieldJ-integral values associated with the subcritical crack growths in fatigue precracked 7075-T6 and blunt notched and fatigue precracked 2024-0 and 5052-H32 aluminum, single-edged notch (SEN) specimens. The initial phases of theJ-resistance curves for the somewhat brittle 7075-T6 and the two ductile 2024-0 and 5052-H32 aluminum SEN specimens are presented. Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.     

K-ε-T model of dense liquid-solid two-phase turbulent flow and its application to the pipe flow

To predict the characteristics of dense liquid-solid two-phase flow, K-ε-T model is established, in which the turbulent flow of fluid phase is described with fluid turbulent kinetic energy K_f and its dissipation rate ε_f, and the particles random motion is described with particle turbulent energy K_p and its dissipation rate ε_p and pseudothermal temperature T_p. The governing equations are also derived. With K-ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.     

Three-dimensional crack tip deformation measurement using combined Moiré-Sagnac interferometry

A combined Moiré-Sagnac interferometry method is developed for in-plane (u andv) and out-of-plane (w) surface deformation measurement. The combined optical setup is used to measure three-dimensional crack tip deformations of AI 2024-0 and AI 2024-T4 specimens at room temperature and an inconel 909 specimen at 570°C. Measured displacements near the crack tip region of the AI 2024-T4 specimen are used as input nodal displacements to determine stress intensity factors based on two-dimensional and three-dimensional Jacobian derivative method. The values compare favorably with theoretical calculations. The extent of the three-dimensional crack tip deformation zone is also discussed.     

Stable crack growth in aluminum tensile specimens

Post's white-light moiré interferometry was used to obtain sequential records of the transientU _y -displacement fields associated with stable crack growth in 7075-T6 and 2024-0, single-edge-notched (SEN) specimens with fatigued cracks. TheU _y -displacement fields are used to evaluate the crack-tip opening displacement (CTOD), far- and near-fieldJ-integral values, Dugdale-strip-yield model, William's polynomial function and the HRR field. Paper was presented at 1985 SEM Spring Converence on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

Determination of all stress components from measurements of the stress invariant by the thermoelastic stress method

A method for the resolution of all stress components from the first invariant J₁ measured by thermoelastic stress analyzer is described. This method may be used to determine, not only surface stress, but also internal stress and stress on the underside.The method is based on the following procedure:

1. (1) Pick an arbitrary domain Ω, within the structure, for which the stresses are required.

2. (2) Measure J₁ on the surface of Ω.

3. (3) Determine the optimum traction along the boundary Γ, which is a part of Ω, by the least squares method such that the difference between the measured J₁ and the calculated J₁ is at a minimum. Either FEM or BEM may be used for this calculation.

Examples of stress resolution for a two-dimensional stress concentration problem and a three-dimensional stress concentration problem are shown. The accuracy of the stress resolution is discussed.     

Analysis of dynamic mixed-mode isochromatics

The mixed-mode, elastodynamic state of stress in the neighborhood of a constant-velocity crack tip is used to generate numerically unsymmetric isochromatics. Unsymmetry associated with the third-order terms of a mixed-mode stress field, with and without the Mode II singular stress term, is also investigated. In extractingK _I from an unsymmetric isochromatic pattern, errors in the Mode I fracture parameters due to the assumed presence ofK _II in aK _I stress field were found to be significant when data are taken more than 4 mm from the crack tip. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Crack linkup: An experimental analysis

TheT _ɛ ^* integral was used to assess stable crack growth and crack linkup in 0.8 mm thick 2024-T3 aluminum tension specimens with multiple site damage (MSD) under monotonic and cyclic loads. TheT _ɛ ^* values were obtained directly from the recorded moiré fringes on the fracture specimens with and without MSD. TheT _ɛ ^* resistance curves of these fracture specimens of different geometries were in excellent agreement with each other. The results suggest thatT _ɛ ^* is a material parameter which can be used to characterize crack growth and linkup in the absence of large overloading.T _ɛ ^* based crack growth and net-section-yield based crack linkup criteria for MSD specimens are proposed. The crack tip opening angle (CTOA) criterion can also be used to correlate crack growth larger than 2 mm.     

Experimental estimation of wall slip for filled rubber compounds

The phenomenon of wall slip during flow of rubber compounds through capillaries is investigated for a typical styrene-butadiene elastomer with carbon black. It was found that at low temperature (110°C) the dependencies of slip velocity V _c on shear stress are described by the power law but, additionally, V _c depends on radius of a channel. At high temperatures there is a critical shear stress below which sliding is absent. Sliding appears only at higher shear stresses where, again, V _c depends on shear stress and the radius of a channel.     

Fatigue crack growth rate in ferrite-martensite dual-phase steel

An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate da/dN when plotted against the effective stress intensity factor range ΔK_eff which was assumed to follow a linear relation with the crack tip stress intensity factor range ΔK. A high ΔK_eff corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor K_cl, however, is affected by the ferrite content with K_cl/Kmax reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite.Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in ΔK and the latter would increase with ΔK depending on the R = σ_min/σ_max ratio. The same data when correlated with the strain energy density factor range ΔS showed negligible dependence on mean stress or R ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and R is introduced for Stage II crack growth so that the da/dN data for different R would collapse onto a single curve with a narrow scatter band when plotted against αΔS.     

Long-term strength of metals in complex stress state (a survey)

An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σ _e is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σ _e on the principal stresses. Statistical methods are used to obtain an expression for σ _e, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σ _e by using additional material constants are considered.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

Influence of stress triaxiality and temperature on void growth and ductile/brittle transition behavior of 40 Cr steel

Examined experimentally are the influence of stress triaxiality and temperature on the growth of microvoids and the ductile/brittle transition (DBT) macrobehavior of 40 Cr steel subjected to two different heat treatments. This is accomplished by testing more than 300 smooth and notched specimens over a temperature range of 20°C to −196°C. Changes in the microstructure morphology are examined by scanning electron microscopy (SEM) and identified with fracture data on a surface constructed from the uniaxial strain ε_c at fracture, the stress triaxiality R_σ and the temperature T. While stress triaxiality has a significant influence on the DBT temperature T_c, it does not affect the ratio of the average radius of voids R_o to that of inclusions R_i. The ratio R_o/R_i is found to increase with temperature and remains constant in specimens with different notch radii regardless of the temperature. Empirical relations between T_c and R_σ⁻ and R_o/R_i and T are proposed to better understand how macrofracture parameters are influenced by microstructure entities.     

Rail web fracture in the presence of residual stresses

A recent accident involving roller-straighened alloy rail has raised the question of the safety of such rails. This work shows that the residual stresses in roller-straightened rail can indeed self-drive a long web crack. Specifically, the stress intensity K_I due to release of the key component, longitudinal stress, if of the order of the critical stress intensity for initiation K_Ic for both plain carbon and alloy rail. At cut ends, the resulting vertical residual stresses can give rise to K_Ic if there are 0.1–1 in (3–25 mm) cracks. In this work, checks of the existing residual stress data for self-consistency suggest that the data are only accurate within a factor of two. Therefore, a more direct method is proposed for measuring K_I on a web crack by saw-cutting the web.     

Range-pair-counting fatigue gage

In this paper, the surface roughening phenomenon of an aluminum foil during fatigue process is utilized for monitoring of a variable amplitude stress. It is found that constant mean stress does not affect surface roughness. When the mean stress varies, however, it causes surface roughening. In such a case, the equivalent stress defined by (Σσ _i ^α N _i /ΣN _i )^1/α dominates surface roughness of an aluminum foil, where σ _i andN _i are stress amplitude and the number of cycles counted by the rangepair method, respectively, and α is a gage factor which is peculiar to the foil used. It is concluded that the aluminum foil can be used as the range-pair counting fatigue gage with high accuracy.     

Plane-strain state of an elastoplastic body with a crack under mixed-mode loading

A mixed-mode (I + II) crack model with a plastic strip on its continuation under plane strain is proposed. The stress components within the strip are determined from the yield conditions, stress limitation, and relationship between the normal stress components defined via the principal stress state. The crack parameters are analyzed for the Mises yield condition. In the quasibrittle case, the governing system of equations includes stress intensity factors K _I, K _II, and T-stresses     

Thermoelastic investigations for fatigue life assessment

An investigation is presented on the suitability and accuracy of a thermoelastic technique for the analysis of fatigue cracks. The stress intensity factor ranges ΔK _I and ΔK _II are determined from thermoelastic data recorded from around the tip of a sharp slot in a steel specimen under biaxial load, in order to assess the accuracy of the technique. ΔK _I and ΔK _II are determined to within 4% and 9% of a theoretical prediction, respectively. The results from a similar test on a fatigue crack under biaxial load are also presented. These show that thermoelastic stress analysis is a rapid and accurate way of analyzing mixed-mode fatigue cracks. A discussion is given on the potential of thermoelastic stress analysis of propagating cracks.