The growth of fatigue cracks through particulate sic reinforced aluminum alloys

Crack growth rates for large fatigue cracks in 12 variations of particulate silicon carbide reinforced aluminum alloy composites have been measured. Composites with seven different matrix alloys were tested, four of which were of precipitation hardening compositions, and those were tested in both as-extruded and peak aged conditions. Five of the materials were made by casting, ingot metallurgical methods and two of the alloys by mechanical alloying, powder metallurgical methods. For both manufacturing methods, primary fabrication was followed by hot extrusion. The fatigue crack growth curves exhibited an approximately linear, or Paris law, region, fitting the function da/dN = BΔK^s, and a threshold stress intensity factor, ΔK_th. As has been found for other materials, the coefficients B and s are correlated; for these composites In B= −16.4−2.1s. A correlation was also found between ΔK_th and s, and it was found possible to compute the magnitude of ΔK_th using a simple model for the threshold together with yield stress and SiC size and volume fraction. These results were explained using a relationship between ΔK_th and crack closure determined previously for unreinforced aluminum alloys. The path of fatigue crack growth is through the matrix for these composites, and SiC has the effect of altering the slip distance, therefore, the plasticity accompanying fatigue cracks. It was shown that all the crack growth rate curves were reduced to one equation having the form da/dN = B'ΔK_eff^s' where B' = 6.5 × 10^-9m/cy and s' = 1.7. A partly theoretical method for predicting fatigue crack growth rates for untested composites is given. Fatigue crack surface roughness was measured and found to be described by a fractal dimension, but no correlation could be obtained between surface roughness parameters and ΔK_th.     

Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6

Fatigue crack initiation and growth characteristics under mixed mode loading have been investigated on aluminum alloys 2017-T3 and 7075-T6, using a newly developed apparatus for mixed mode loading tests. In 2017-T3, the fatigue crack initiation and growth characteristics from a precrack under mixed mode loading are divided into three regions—shear mode growth, tensile mode growth and no growth—on the ΔK_I-ΔK_II plane. The shear mode growth is observed in the region expressed approximately by ΔK_II > 3MPa√m and ΔK_II/ΔK_I > 1.6. In 7075-T6, the condition of shear mode crack initiation is expressed by ΔK_II > 8 MPa√m and ΔK_II/ΔK_I > 1.6, and continuous crack growth in shear mode is observed only in the case of ΔK_I/ΔK_II, 0. The threshold condition of fatigue crack growth in tensile mode is described by the maximum tensile stress criterion, which is given by Δσ_θmax √2πr 1.6MPa√m, in both aluminum alloys. The direction of shear mode crack growth approaches the plane in which K_I decreases and K_II increases towards the maximum with crack growth. da/dN-ΔK_II relations of the curved cracks growing in shear mode under mixed mode loading agree well with the da/dN-ΔK_II relation of a straight crack under pure mode II loading.     

Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor

The relationship between fatigue crack propagation rate, da/dn, and range of stress intensity factor, ΔK, including threshold stress intensity factor, ΔK_th, is analyzed statistically. A non-linear equation, da/dn = C{(ΔK)^m-(ΔK_th)^m}, is fitted to the data by regression method to evaluate the 99% confidence intervals. Several experimental results on fatigue crack propagation properties of welded joints are compared by using these confidence intervals.     

Influence of R on effective stress range ratio and crack growth

The influence of stress ratio R and stress intensity range ΔK on crack closure and fatigue crack growth were studied. Crack closure and crack growth experiments were performed on 6063-T6 Al alloy. Crack closure stresses were measured using a surface-measurement technique with a COD gauge. The gauge was placed at different locations behind the crack tip, and it was found that the location of the gauge does not influence the closure load. The closure load was however found to be a function of R and ΔK. Fatigue crack growth rate is found to depend upon R, U and ΔK. A model for both U and da/dN has been developed.     

Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

Influence of stress ratio at baseline loading on delayed retardation phenomena of fatigue crack growth in A553 steel and A5083 aluminium alloy

The delayed retardation phenomena of fatigue crack growth following a single application of tensile overload were investigated under the baseline loading with the stress ratio, R = σ_min/σ_max, ranging from −1 to 0.5 for A553 steel and A5083 aluminium alloy. Two different overload cycles were applied; the one is the case that the ratio of peak stress range to baseline stress range, r = Δσ₂/Δσ₁, is equal to two and the other is the case that the ratio of maximum peak stress to maximum baseline stress, σ_2max/σ_1max, is equal to two. The retardation took place stronger in aluminium than in steel. Under the condition of r = 2 the normalized number of cycles, N_D/N_C, (N_D: the number of cycles during retardation, N_C: the number of cycles required for propagation through the overload-affected-zone size) decreased slightly as the R ratio increased from −1 to 0.5, while under the condition of σ_2max/σ_1max = 2 the N_D/N_C-values increased drastically as the R ratio increased from −1 to 0 (or the overload ratio, r, increased from 1.5 to 2) in both the materials. These retardation behaviors were expressed theoretically according to the model proposed by Matsuoka and Tanaka [1, 3] by using four parameters: the overload ratio, r, the exponent in Paris equation, m, the overload-affected-zone size, ω_D, and the distance at the inflection point, ω_B.     

Study of crack tip opening under cyclic loading taking into account the environment and R ratio

This study involves the R effect and environment effect on crack closure mode, in 7175 T 651 aluminium alloy. To obtain one of the selected objectives, it was necessary to use a clip gauge located at the notch of the compact specimen and a C.T.O.D. gauge located at the crack tip. The crack opening phenomena observed in our tests depends on the applied method which accounts for the differences in ΔK_eff found in the literature. The systematic use of the two methods allowed us to bring to light common features permitting the calculation of ΔK_eff according to Elber's criteria. The concept of ΔK_eff does not fully explain the influence of R ratio and the environment effect.     

Enhancement of delayed failure resistance by partial unloading method

The effects of two types of pre-stressing, i.e. partial unloading (0 →K_max → K) and perfect unloading (0 → K_max → 0 → K) on the delayed failure strength were investigated using pre-cracked specimens of JIS SNCM8 steel quenched and tempered, where K_max is the maximum stress intensity factor at pre-stressing, and K is the stress intensity factor under which delayed failure test is carried out.

Both pre-stress methods can markedly increase the delayed failure strength or the lower limit stress intensity factor K_ISCC. The partial unloading method is superior to the perfect unloading method in each tempering condition (200 or 400°C) and in each environment (distilled water or 3% NaCl water). The reason why K_ISCC is increased by each pre-stressing can be explained by the decrease of surface stress at crack tip, which will suppress the corrosion reaction and prevent the invasion of hydrogen atoms into the material.     

Fatigue crack growth characteristics of rotor steels

Room temperature fatigue crack growth rate data were generated for Ni-Mo-V (ASTM A469, Cl-4), Cr-Mo-V (ASTM A470, Cl-8) and Ni-Cr-Mo-V (ASTM A471, Cl-4 and a 156,000 psi yield strength grade) rotor forging steels. Testing was conducted with WOL type compact toughness specimens and the results presented in terms of fracture mechanics parameters. Data show that the Ni-Cr-Mo-V steels exhibit slower fatigue crack growth rates at a given stress intensity range (ΔK) than do the Ni-Mo-V steels. In addition, the Cr-Mo-V steel was found to exhibit slower growth rates than the other alloys at ΔK levels below 40 ksi √in but somewhat foster rates at ΔK levels in excess of 45 ksi √in. The fatigue crack growth rate properties of the alloys studied conform to the generalized fracture mechanics crack growth rate law where da/dN = C₀ΔK^R. It was noted that the fatigue crack growth rate parameters n and C₀ tend to decrease and increase, respectively, with increasing material toughness, K_ic.     

Effect of temperature on the frequency dependency of crack propagation velocity in delayed failure under cyclic load

The crack propagation velocity and the incubation time in delayed failure under repeating load were examined at various frequency ƒ(0–800 cpm) and temperature T(5–80°C) using the pre-cracked specimen of JIS SNCM8 quenched and tempered. The crack propagation velocity under repeating load (da/dt)_R decreased with increase of frequency ƒ and revealed a minimum value (da/dt)_minat a certain ƒ. The activation energy obtained from the Arrhenius plot of (da/dt)_min vs 1/T was about 10,000 cal/mol, which was a little larger than 8100 cal/mol obtained from the relation between the crack propagation velocity under static load and 1/T. The reason for the existence of the minimum value in the crack propagation velocity was explained by assuming the interaction between hydrogen atoms invaded from crack tip and the cyclic change of the position with tri-axial tensile stress. The incubation time under repeating load did not seem to be controlled by the diffusion or concentration process of hydrogen atoms.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

Representation of the displacement rate between the loading points in terms of applied stress and temperature and its relation to creep crack growth rate, C, P and Q parameters

The displacement rate between the loading points in SUS 304 stainless steel has been experimentally obtained under several applied gross stress and high temperatures, and the equation for has been obtained experimentally as a function of applied gross stress σ_g and absolute temperature T. Then, the relation of δ to creep crack growth rate da/dt was clearly shown in terms of equation. Furthermore, the relation has been clarified between the energy rate line integral C^* as affected by , and P parameter. In this way, it is clearly shown why log (da/dt) data plotted against log C^* deviates in some systematic trend with the increase of temperature and gross stress, respectively, whereas log da/dt vs the P parameter becomes exactly the same and one straight line independent of temperature and gross stress. The discussion is made on that the similar relation will hold between the evaluation by C^* and that by _gQ or by Q^*.     

Temperature dependence of stage II fatigue crack growth rate

A critical assessment has been performed by compiling experimental data concerning the temperature dependence of stage II fatigue crack growth. For aluminium alloys, high strength steels, austenitic stainless steels and superalloys, the power coefficient, m, for the Paris relationship is temperature dependent and all ln(da/dN) vs ln(ΔK) curves cross at one point, designated as the pivot point (PP), which is a material-dependent parameter. The assumption is made that PP corresponds to a transition point for the fatigue crack growth mechanism.     

Shear lips on fatigue fractures in aluminium alloy sheet material

An analysis is made of shear lip width measurements and the transition of tensile mode fatigue cracks to shear mode fatigue cracks, as observed on fatigue crack surfaces of aluminium alloy sheet material. It could be shown that these phenomena were controlled by ΔK_eff, rather than K_max or ΔK. For crack growth in air the shear lip width was approximately proportional to (ΔK_eff)², but it was significantly larger than the estimated size of the reversed plastic zone. The initiation of shear lips, the transition from plane stress to plane strain along the crack front and the environmental effect on shear lips are briefly considered in the discussion.     

A microcomputer control system for the measurement of fatigue crack growth data

A microcomputer-based system for the measurement of fatigue crack growth da/dn versus cyclic stress intensity factor ΔK data using compact-tension test specimens is described. The procedure has been developed to allow automatic measurement of crack growth rate under any specified combination and sequence of load conditions, i.e. ΔK and R (stress ratio) and includes the capability of establishing the threshold cyclic stress intensity factor ΔK₀. Crack extension measurement is effected from the elastic compliance evaluated from the AC component of the load and displacement signals to an accuracy of -3 μm every 1000 load cycles. Results from a typical low-alloy-steel rotor forging are presented to illustrate the use of the system.     

The solution of a displacement discontinuity for an anisotropic half-plane and its applications to fracture mechanics

By imaginal method the solution of displacement discontinuity for anisotropic half-plane is derived in this paper. According to the Betti's reciprocal theorem, the relationship between the stress intensity factor K_I and the increment Δv/Δa is established and numerical results of K_I are obtained by the twice calculation method. Furthermore, the problem of edge crack chopping is studied in great detail, and the area of contaction and stress intensity factor K_I are found. These results are very worthwhile for research of chopping fracture in theory.     

A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns

A general method is presented for determining mixed-mode stress intensity factors K_I and K_II from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non-singular stress, σ_ox. A non-linear equation is developed which relates the stress field in terms of K_I, K_II, and σ_ox to the co-ordinates, r and θ, defining the location of a point on an isochromatic fringe of order N.

Four different approaches for the solution of the non-linear equation are given. These include: a selected line approach in which data analysis is limited to the line θ = π and the K---N relation can be linearized and simplified, the classical approach in which two data points at (r_m, θ_m) are selected where r_m/θ = 0; a deterministic method where three arbitrarily located data points are used; and an over-deterministic approach where m (>3) arbitrarily located points are selected from the fringe field.

Except for the selected line approach, the method of solution involves an iteractive numerical procedure based on the Newton-Raphson technique. For the over-deterministic approach, the method of least squares was employed to fit the K-N relation to the field data.

All four methods provide solutions to 0.1% providing that the input parameters r, θ, and N describing the isochromatic field are exact. Convergence of the iterative methods is rapid (3–5 iterations) and computer costs are nominal. When experimental errors in the measurements of r and θ are taken into consideration, the over-deterministic approach which utilizes the method of least squares has a significant advantage. The method is global in nature and the use of multiple-point data available from the full-field fringe patterns permits a significant improvement in accuracy of K_I, K_II, and σ_ox determinations.     

Fatigue crack-growth characteristics of two magnesium alloys

Magnesium alloys are being increasingly used for engineering applications. Fatigue crack-growth data have therefore been obtained for a high strength magnesium-Zr alloy and a medium strength, weldable magnesium-Mn alloy. The results of tests on sheet material are presented in terms of the range of stress intensity factor ΔK. Critical values of ΔK necessary for fatigue crack growth ΔK_c were also obtained. The behaviour of the two alloys was similar; both rates of crack growth and ΔK_c were sensitive to mean stress. Fatigue crack growth was entirely on a 90° plane with no sign of the transition to crack growth or 45° planes usually observed in sheet materials. This was ascribed to the effects of preferred orientation of the crystal structure.     

Relaxation of residual stress with fatigue loading

Investigations have been carried out to study the relaxation of the surface residual stress in 0.23% C steel due to the application of fatigue loading. The residual stress was induced in the specimen by pre-straining and was measured by X-ray back reflection method using Cr-K radiation. The surface residual stress induced, depends on the plastic strain and appears to bear a relation of the type σ_R = σ_o(e_p)^0.78. The decay of the residual stress appears to depend on log N, given by the relation σ_R1 = σ_RO−K log N, where N is the number of fatigue cycles. The constant K depends on the initial value of the residual stress.     

Hardness, internal stress and fracture toughness of epitaxial AlxGa1−xAs films

Vickers microhardness indentations of 10 μm (001) oriented epilayers of Al_xGa_1−xAs on GaAs substrates have been utilized to evaluate the hardness H_v, the internal stress, and the fracture toughness K_Ic of the layers as a function of their composition parameter x. The hardness H_v varies linearly according to: (6.9-2.2x) GPa and K_Ic increases linearly with x according to: K_1c = (0.44+1.30x) MPa m^1/2. The influence of the substrate on these measurements was found to be negligible for the layer thickness (10 μm) and the indentation load (0.25 N) used, disregarding internal stresses.

Internal film stresses were evaluated by the bimorph buckling method, and were found to depend on the composition parameter according to σ = 0.13x GPa. These stresses did not notably affect the H_v measurements, but for K_Ic corrections as large as 25% had to be made.

The radial cracks observed were of the shallow Palmqvist type. In contradiction to previous reports on this type of cracking, it was found to initiate during unloading, not during loading, and a physical explanation for this deviation is given. No deep radial/median cracks were observed. It was found important to use expressions based on the correct crack geometry in the K_Ic evaluation. Also, a simple theory for the influence of internal stresses on the K_Ic results has been developed.