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.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

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.     

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring.In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ^*, d^* and σ^* are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ^*, d^* and σ^* and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale.The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a₀. Large ξ (0.90 and 0.85) gives critical crack size a_cr = 11–14 mm (at t < 20 yr) for a₀ about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a_cr = 6–7 mm (at t < 20 yr) for a₀ about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a_cr and a₀ can be made to meet the condition oft = 20 yr.Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.     

Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δk_th increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is k_max and σ_ys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10^—8 to 10⁻⁷ mm/cycle.A dimensionless relation of the form for collating fatigue crack starting growth data is proposed in which Δk_th represents the stress intensity factor range at the threshold. Based on experimental results, this relation attains the value of 0.6 for a fatigue crack to start growth in the Austenitic stainless steel investigated in this work. Metallurgical examinations were also carried out to show a transgranular shear mode of cyclic cleavage and plastic shear.     

On thermodynamic potentials in linear thermoelasticity

The four thermodynamic potentials, the internal energy u=u(ε_ij,s), the Helmholtz free energy f=f(ε_ij,T), the Gibbs energy g=g(σ_ij,T) and the enthalpy h=h(σ_ij,s) are derived, independently of each other, by using the Duhamel–Neumann extension of Hooke's law and an assumed linear dependence of the specific heat on temperature. A systematic procedure is then presented to express all thermodynamic potentials in terms of four possible pairs of independent state variables. This procedure circumvents a tedious transition from one potential to another, based on the formal change of variables, and inversions of the stress–strain and entropy–temperature relations. The general results are applied to uniaxial loading paths under isothermal, adiabatic, constant stress, and constant strain conditions. An interplay of adiabatic and isothermal elastic constants in the expressions for exchanged heat along certain thermodynamic paths is indicated.     

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.     

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.     

Effect of transverse cracks on the mechanical properties of angle-ply composites laminates

A modified shear lag analysis, taking into account the notion of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in [±θ_n/90_m]_S angle-ply laminated composites. Effects of number of 90° layers and number of ±θ layers on the laminate stiffness have also been studied. The present results represent well the dependence of the degradation of mechanical properties on the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of uncracked outer ±θ layers in the laminate.     

Effects of deformed volume, volume fraction and particle size on the deformation behaviour of W/Cu composites

Tungsten/copper (W/Cu) particle reinforced composites were used to investigate the scaling effects on the deformation and fracture behaviour. The effects of the volume fraction and the particle size of the reinforcement (tungsten particles) were studied. W/Cu-80/20, 70/30 and 60/40 wt.% each with tungsten particle size of 10 μm and 30 μm were tested under compression and shear loading. Cylindrical compression specimens with different volumes (D_S = H) were investigated with strain rates between 0.001 s⁻¹ and about 5750 s⁻¹ at temperatures from 20 °C to 800 °C. Axis-symmetric hat-shaped shear specimens with different shear zone widths were examined at different strain rates as well. A clear dependence of the flow stress on the deformed volume and the particle size was found under compression and shear loading. Metallographic investigation was carried out to show a relation between the deformation of the tungsten particles and the global deformation of the specimens. The size of the deformed zone under either compression or shear loading has shown a clear size effect on the fracture of the hat-shaped specimens.The quasi-static flow curves were described with the material law from Swift. The parameters of the material law were presented as a function of the temperature and the specimen size. The mechanical behaviour of the composite materials were numerically computed for an idealized axis-symmetric hat-shaped specimen to verify the determined material law.     

Quasi-static behavior of Mg-alloys with and without short-fiber reinforcement

Magnesium alloys AE42 and AZ91 reinforced with 23 vol.% carbon short fibers (D_f ≈ 7 μm, L_f ≈ 100 μm) were tested under quasi-static loading. The carbon fibers were quasi-isotropically distributed in the horizontal plane (reinforced plane) of the casting. Compression and tensile tests were carried out on both the matrix alloys and the composites at temperatures between 20 °C and 300 °C. Specimens were machined to be loaded either parallel or normal to the reinforced plane. Due to the reinforcement, the compression yield stress of the composite AE42-C increased to a value approximately three-fold greater than the yield strength of the matrix; for composite AZ91-C this parameter was approximately 2.5-fold greater than that of the AZ91 matrix. The improvement in tensile strength was less than that in compression, which could be related to early tensile fracture through decohesion at the matrix–fiber interface, as detected by SEM investigations conducted on failed tensile specimens. Flow curves for the matrix alloys at different temperatures were described by a modified Kocks–Mecking material law. An idealization of a 2-D mesomodel was used for finite-element simulation of the mechanical behavior of the composites. The fibers were first considered as elastic bodies and the behavior of the matrix material was set according to the material law determined from the flow curves for the matrix alloys. Other calculations were carried out by considering elasto-plastic behavior of the fibers for application of a failure initiation technique to simulate the behavior of the composite materials beyond the ultimate stress.     

Mechanics of adhesive contact on a power-law graded elastic half-space

We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E=E₀(z/c₀)^k (0<k<1) while Poisson's ratio ν remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of P_cr=−(k+3)πRΔγ/2 where Δγ is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k=0, the Gibson solid when k→1 and ν=0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off.     

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

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.     

Flexural fatigue behavior of threaded connections for large diameter pipes

Full-scale flexural fatigue tests were conducted to investigate the fatigue behavior of a patented threaded connection for large diameter (0.61 m (24 in) outside diameter, 25.4 mm (1 in) wall thickness) offshore pipes. Fifteen fatigue tests were performed by subjecting the threaded connection to constant amplitude stress ranges (between 69 MPa (10 ksi) and 151.8 MPa (22 ksi) on gross cross section) with zero mean stress. The corresponding measured fatigue lives varied from 45000 to 4852200 cycles. Fatigue failures were in the form of cracks through the thickness of the wall and located at the root of the first full contact thread. The failure surfaces were ‘typical’ with identifiable zones of crack initiation, propagation and fracture. Linear regression analysis of the experimental results, namely the applied stress range (S _r ) and the measured number of cycles to failure (N) data, in the log-log domain gave anR ² value of 0.88 and the least-squares best fit equation asS _r (MPa)=1573.2N ^−0.212. The 90% probable fatigue strength prediction equation was estimated asS _r =1393.8N ^−0.212. This equation is recommended for design purposes.     

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.     

Fatigue crack growth studies in rail steels and associated weld metal

Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth.In rail steel microstructures at low ΔK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at K_max values approaching 40 MPa √m transgranular cleavage facets initially formed and their incidence increased with K_max until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60–100 μm.The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all ΔK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 μm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.