A basic study of a strain gage made of nickel foil

Strain gages made of nickel foil are devised for measuring the elastic surface stress of a specimen subjected to repeated loads. Sticking nickel foil on the surface of a specimen, the elastic stress is measured by observing slip-bands in the foil resulting from repeated strains. Calibration studies with rotating-bending tests are performed on round steel bars with nickel foil to determine the applicable test temperatures for the gage, and to establish the relation between the first appearance of slip-bands and the magnitude of cyclic stress. The peak stresses in grooved shafts under bending are measured with the nickel foil gages. The accuracy of the results is examined.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Near critical phenomena in laminar boundary layers

Asymptotic analysis of boundary layer separation in the limit of large Reynolds number Re→∞ has shown that in a number of cases which are of importance from a practical point of view solutions of the resulting interaction equations describing two-dimensional (2-D) steady flows exist up to a limiting value Γ_c of the relevant controlling parameter Γ only while two branches of solutions exist in a regime Γ<Γ_c. The present study aims at a better understanding of near critical flows |Γ-Γ_c|→0 and in particular the changes of the flow behaviour associated with the passage of Γ through Γ_c.     

Fatigue crack opening stress based on the strip-yield model

The modified strip-yield model based on the Dugdale model and two-dimensional approximate weight function method were utilized to evaluate the effect of in-plane constraint, transverse stress, on the fatigue crack closure. The plastic zone sizes and the crack opening stresses considering transverse stress were calculated for four specimens: single edge-notched tension (SENT) specimen, single edge-notched bend (SENB) specimen, center-cracked tension (CCT) specimen, double edge-notched tension (DENT) specimen under uniaxial loading. And the crack opening behavior of the center-cracked specimen under biaxial loading was also evaluated. Normalized crack opening stresses σ_op/σ_max for four specimens were successfully described by the normalized plastic zone parameter Δω^′_rev/ω^′ considering transverse stress, where Δω^′_rev and ω^′ are the size of the reversed plastic zone at the moment of first crack tip closure and the size of the forward plastic zone for maximum stress, respectively. The normalized plastic zone parameter with transverse stress also was satisfactorily correlated with the behavior of crack closure for CCT specimen under biaxial loading.     

Stretch and twist of rotating prismatic beam

A turbine blade is modelled as a uniform isotropic prismatic beam of general cross-section and “setting angle” rotating about one end, and is analysed according to the linear theory of elasticity. A semi-inverse solution is presented which reduces the three-dimensional problem to one of two dimensions, and explicit stress and strain components given for the mathematically amenable elliptic cross-section. As expected, the planar stresses σ_x,σ_y, and τ_xy arising from the two-dimensional problem are found to be small. For the general section, the theory predicts small curvature of the blade centre line, and a twisting moment which tends to reduce the “angle of set”.     

A centrally cracked thin circular disk, Part I: 3D Elastic–plastic finite element analysis

A full field solution, based on small deformation, three-dimensional elastic–plastic finite element analysis of the centrally cracked thin disk under mode I loading has been performed. The solution for the stresses under small-scale yielding and lo!cally fully plastic state has been compared with the HRR plane stress solution. At the outside of the 3D zone, within a distance of rσ_o/J=18, HRR dominance is maintained in the presence of a significant amount of compressive stress along the crack flanks. Ahead of this region, the HRR field overestimate the stresses. These results demonstrate a completely reversed state of stress in the near crack front compared to that in the plane strain case. The combined effect of geometry and finite thickness of the specimen on elastic–plastic crack tip stress field has been explored. To the best of our knowledge, such an attempt in the published literature has not been made yet. For the qualitative assessment of the results some of the field parameters have been compared to the available experimental results of K, gives a fair estimate of the crack opening stress near the crack front at a distance of order 10⁻² in. On the basis of this analysis, the Linear Elastic Fracture Mechanics approach has been adopted in analyzing the fatigue crack extension experiments performed in the disk (Part II).     

Fatigue life prediction of out-of-plane gusset welded joints using strain energy density factor approach

Fatigue growth behavior of out-of-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests on two types of specimens with curvatures of ρ = 0 and ρ = 30 were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis is carried out to show the effects of initial crack shape, initial crack length and stress ratio. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes. The results of analysis for the assumed crack shapes agreed well with the experimental data. Fatigue propagation life of the ρ = 30 specimen was larger than that of the ρ = 0 specimen.     

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 on small scale bridging in fibrous monolithic ceramics

Based on shear lag model of interface between fiber and matrix, a new formula that relates the crack opening displacement and bridging force in fibrous monolithic ceramics was constructed under the framework of small scale bridging. This formula was applied to predict the fracture resistance orR-curve response of a three-point bending specimen made of fibrous monolithic ceramics. A parametric investigation on the influences of fiber volume fraction, fiber radius, characteristics of constituents, BN's fracture toughness and specimen's geometry on the bridging forces and fracture resistance in Si₃N₄/BN composite was carried out. The upper and lower limits of theR-curve of Si₃N₄/BN in small scale bridging were derived. This research revealed the role played by the above parameters in the fracture toughness of fibrous monolithic ceramics. Supported by National Natural Science Foundation of China (59632090).     

Comparisons of different procedures of pre-compaction stress determination on weakly structured soils

Compaction is an important component of soil degradation. In this regard, the pre-compaction stress (σ_pc) concept is considered useful in mechanized agriculture nowadays. When the external forces exceed the internal strength (σ_pc) of soil, soil structure and soil physical quality will deteriorate. This concept was introduced at first for confined consolidation of non-structured, homogenized and saturated subsoils in civil engineering, though it is also suitable for agricultural conditions where the topsoil and subsoil are considered and both are often structured, heterogeneous and unsaturated. The best method for predicting σ_pc is by the plate sinkage test (PST) in the field, but it is expensive and time-consuming. This study was conducted to find an alternative laboratory method besides the confined compaction test (CCT) for predicting σ_pc. The CCT may not be a good method, especially at higher water contents, and for soils with low organic matter content, because of low sharpness of the critical region on the stress–strain curves. The study was performed on five soil types with a range of soil textures and organic matter content from central Iran using three loading types and three pF (i.e. Log [soil matric suction in cm]) values of 2.3, 2.7 and 2.9 with two replicates. Loading types consisted of CCT, the semi-confined compaction test (SCCT) and the kneading compaction test (KCT) at three maximum (or pre-compaction) stresses of 200, 400 and 600 kPa. The experiment was a completely randomized factorial design. The aim was to determine how accurately each loading type test could predict σ_pc of soil pre-compacted by one of the other methods. The applied combinations of CCT–SCCT, SCCT–CCT and KCT–CCT mean that the soil was pre-compacted by the first loading type and evaluated by the second one. The results showed that σ_pc and the sharpness of the σ_pc region were significantly affected by loading types as well as the soil conditions. The sharpest σ_pc region was observed in SCCT and the least sharp in CCT with the overall order being CCT–SCCT > SCCT–CCT > KCT–CCT. The sharpness of the σ_pc region was reduced for the soil samples with higher water content and coarser texture. Regardless of the soil and loading conditions, the prediction by SCCT was consistently more accurate than by CCT. The prediction of σ_pc by SCCT was more precise in comparison with CCT especially at higher stresses and soil water contents. However, the prediction of σ_pc by SCCT was very accurate at pF values of 2.7 and 2.9, and with low σ_pc values, when compared with the actual values of the σ_pc. For the clay soil at a pF value of 2.3, no pre-compaction region (i.e. zero σ_pc) could be determined by CCT at a maximum axial stress of 600 kPa. This was because of the incompressibility of soil water at this near-saturated soil condition at high stress. However, the sharpness of the critical region in SCCT was high enough to predict σ_pc satisfactorily. There was no significant difference between the combinations of SCCT–CCT and KCT–CCT in predicting σ_pc. The SCCT is a compromise method that lies between CCT and PST. SCCT has the advantage of using a limited and definite soil volume that can be modeled as a soil element. Marginal effects of disturbance caused by coring/sampling as well as pre-test sample preparation seem to have minor effects on the stress–strain curve determined by SCCT in comparison with CCT. Moreover, the soil volume needed for this test is the same as for CCT.     

Influence of singularity dominated zone for propagating cracks in finite size specimens

The singularity dominated zones for straight as well as curved cracks propagating in finite size specimens were determined experimentally by using the optical method of dynamic photoelasticity using the near-field stress equations. Experimental data was carefully analyzed using improved numerical schemes to get the complete stress field around the propagating crack. This stress field was critically examined to evaluate the size of singularity dominated zones for cracks propagating in straight as well as curved paths. For this purpose, the exact solution was compared with the singular solution using stress components σ_x, σ_y, τ_xy and the maximum shear stress τ_max as a criterion respectively. For straight cracks where the stress field is symmetric about the crack path, the singularity dominated zones can be determined by using any one of the stresses. However, for a curved crack, the zones were unsymmetric. This study shows that σ_y, the crack opening stress, yields the best result for characterizing the singularity dominated zone around a running crack tip.     

Stress intensity factors and crack initiation directions for ceramic/metal joint

Four points bending tests for Si₃N₄/Cu/S45C joint specimen showed that the bending strengths depend on the residual stresses that originated from joining process. The residual thermal stresses caused an edge sub-interface crack to initiate in the ceramic. The stress intensity factors (SIFs) of the edge sub-interface crack located at distance h from the interface with or without interlayer metal were calculated by the Green's function obtained from a finite element analysis. The crack path at the joint specimen under four points bending loading with the influence of residual stresses was also evaluated by the maximum tensile stress criterion. Finally the effect of residual stress on the crack path was found numerically; the interlayer metal decreases the deflection angle of crack from interface by reducing the residual stress.     

Fatigue behavior of E-glass fiber reinforced phenolic composites: effect of temperature, mean stress and fiber surface treatment

Phenolic matrix is reinforced by unidirectional E-glass fibers with volume fractions of 0.30 and 0.45. Three different surface treatments are applied to the E-glass fibers. The composite specimens are tested at ambient condition and temperatures of 100°C 150° and 200°C with stress levels of R(σ_min/σ_max) equal to 0 and 0.4 for load frequencies of 1.5, 10 and 25 Hz. Data are presented in terms of S/N curves and assessed by degradation of modulus based on compliance. For a particular fiber glass surface treatment and volume fraction, the composite specimen is notched and tested at room temperature and 200°C. A fatigue strength reduction factor K_f is defined and obtained such that the results could be compared with those of the unnotched specimens. Notch effect is small if the hole diameter is equal to the specimen thickness; it would be important for larger hole sizes. Fractured surfaces are examined by the scanning electron microscope.     

Loading rate spectra for fracture initiation in metals

In the first part of the paper a review of experimental results is presented on the effects of loading rate of the fracture initiation toughness of structural alloys. Recent progress in new experimental techniques enables for measuring the fracture initiation properties over ten orders of magnitude in , where loading rate for plane strain fracture toughness. The range covered in experiments is

Full-size image (1K)

.Experimental results for aluminum and titanium alloys, as well as for some steels are discussed. Those results are shown as loading rate spectra where the fracture toughness K_Ic is plotted versus log at constant temperature. The patterns of the loading rate spectra demonstrate a negative role of the strain rate sensitivity in the process of fracture initiation, at least within a certain ranges of the loading rate .In the second part an attempt is presented to model the observed phenomena. Consequently, a new model has been proposed which combines an semi-empirical correlation between the critical fracture stress σ_F, yield stress σ_y from one side and a simple thermally activated potential of plastic flow from the other. It has been demonstrated that this simple approach can predict properly a fundamental changes in the loading rate spectra for steels.     

Crack size and speed interaction characteristics at micro-, meso- and macro-scale

The motivation to examine physical events at even smaller size scale arises from the development of use-specific materials where information transfer from one micro- or macro-element to another could be pre-assigned. There is the growing belief that the cumulated macroscopic experiences could be related to those at the lower size scales. Otherwise, there serves little purpose to examine material behavior at the different scale levels. Size scale, however, is intimately associated with time, not to mention temperature. As the size and time scales are shifted, different physical events may be identified. Dislocations with the movements of atoms, shear and rotation of clusters of molecules with inhomogeneity of polycrystals; and yielding/fracture with bulk properties of continuum specimens. Piecemeal results at the different scale levels are vulnerable to the possibility that they may be incompatible. The attention should therefore be focused on a single formulation that has the characteristics of multiscaling in size and time. The fact that the task may be overwhelmingly difficult cannot be used as an excuse for ignoring the fundamental aspects of the problem.Local nonlinearity is smeared into a small zone ahead of the crack. A “restrain stress” is introduced to also account for cracking at the meso-scale.The major emphasis is placed on developing a model that could exhibit the evolution characteristics of change in cracking behavior due to size and speed. Material inhomogeneity is assumed to favor self-similar crack growth although this may not always be the case. For relatively high restrain stress, the possible nucleation of micro-, meso- and macro-crack can be distinguished near the crack tip region. This distinction quickly disappears after a small distance after which scaling is no longer possible. This character prevails for Mode I and II cracking at different speeds. Special efforts are made to confine discussions within the framework of assumed conditions. To be kept in mind are the words of Isaac Newton in the Fourth Regula Philosophandi:

“Men are often led into error by the love of simplicity which disposes us to reduce things to few principles, and to conceive a greater simplicity in nature than there really is … We may learn something of the way in which nature operates from fact and observation; but if we conclude that it operates in such a manner, only because to our understanding that operates to be the best and simplest manner, we shall always go wrong.”––Isaac Newton

Dislocation pile-up model of fatigue thresholds for 2024- and 7075-alike aluminium alloys

Two parameters, K_max^* and δK_th^*, are presented to describe fatigue threshold behaviour and damage under any load ratio without invoking crack closure. Modelled are two fatigue thresholds that are coherently related to fatigue limit δσ_FL; they predict the fundamental threshold curves for aluminium alloys. By using a continuous configuration of dislocations in pile-up, fatigue limit behaviour is simulated as pile-up of dislocations against grain boundaries. A fatigue limit is determined in terms of a critical condition at which a fictitious microcrack associated with the pile-up corresponds to the onset of propagation. These two fatigue thresholds are attainable as the local stresses at the crack front approaching the fatigue limit. Microstructure is incorporated in the model to account for the effect on threshold behaviour. As a result, two fatigue threshold criteria are required. Quantitative assessment of the two criteria requires only knowledge of the conventional material properties in conjunction with microstructure. The micromechanical modelling exhibits a strong dependence of fatigue thresholds upon local microstructure.     

Plasticity of a high strength steel alloy

Experimentally determined plastic constitutive equations of the parabolic form (σ − σ_y = β(ε − ε_y)1/2) are presented for a high strength alloy steel. Two deformation moduli β were required to describe the quasistatic compression data, both of which, as well as the point of change, were predicted by a mode index and transition strain structure of a general theory of plasticity. Dynamic strain, duration of impact, and final strain distribution were measured on specimen rods subjected to axial, symmetric, and constant velocity impact. The dynamic yield stress was 16% higher than the quasistatic value. The dynamic response function, deduced from a simple wave propagation theory, was also parabolic and a single deformation modulus, equal to the initial quasistatic value, applied. Thus, it was shown that the form of the quasistatic response function was preserved in dynamic loading, and that the increase of the dynamic stress was due to the increase of the yield stress.     

Damage of hybrid composites under long term hygrothermal loading and stacking sequence

The exposure of polymeric composite matrix to a cyclic moist environment produces transient residual stresses extremely important at the edges of the laminated plates, particularly at first times. In cases of critical cyclic environmental conditions, the damage of composites becomes very probable, so durability is intensively reduced. To avoid the damage probability, and to reduce the transient hygrothermal stresses, in our paper the hybrid composites with optimal stacking sequences are used. The first aim of this paper is the determination of hygrothermal characteristics for balanced stacking sequences [θ/−θ]_nS. Therefore, in order to locate the favourite directions of each stacking sequence, the polar representation method is adopted. The suitable choice of hygrothermal characteristics, allows thereafter, the reduction of transient hygrothermal stresses. By using the quadratic failure criterion in stress space, the transient strength ratio is evaluated at first ply of the hybrid plate for each sequences [θ/−θ]_nS from initial time until saturation time. Avoid the damage probability is reached by the reduction of transient hygrothermal stresses along the thickness of the hybrid plate. To locate the minimal and maximal stresses, a progressive variation of the relationship between the thicknesses h₁ and h₂ of hybrid composites constituents AS3501 and T300/5208 was carried out. In this way five cases are proposed, on which, the thickness of each material varies gradually, but the total thickness of our plate remains constant. This procedure permits us to find the best configuration which will offer favourable conditions of services, i.e., to predict a considerable reduction of hygrothermal transverse stresses at both edges of the hybrid plate.     

Influence of debonding on the efficiency of crack patching

A simplified analysis of crack patching is presented in which the restraining effect of the external bonded reinforcement on the crack opening is simulated by distributed springs acting between the crack faces. It is suggested that elastic-perfectly plastic springs provide an adequate idealization for the case where debonding can occur. The analysis is thereby reduced to the solution of a one-dimensional integral equation involving only two material parameters: a spring constant k and a limit stress σ_L, both of which can be determined from the behaviour of a suitable overlap joint. The efficiency of the reinforcement is shown to be determined by the normalized crack length ka and the normalized stress σ/σ_L, so that a comprehensive characterization can be obtained from relatively little computation or experimental study.     

Fracture toughness of CIP-HIP Beryllium at elevated temperatures

The fracture toughness of CIP-HIP Beryllium was determined using the short bar fracture toughness (K_IcSB) method. The K_IcSB value measured was 10.96 MPa√m at room temperature. This falls well within the expected range of 9 to 12 MPa√m as observed from previous fracture toughness measurements of beryllium. Toughness increased rapidly between 400°F and 500°F reaching a value of 16.7 MPa√m at 500°F.