Determine Fatigue Crack Growth Research Articles

An innovative approach to planar mixed-mode fatigue crack growth study

Determining fatigue crack growth parameters under mixed-mode loading is crucial for damage tolerance design, particularly in assessing a component's residual life with defects to prevent disasters. This study introduces a novel methodology for determining fatigue crack growth rate. A digital microscope is utilized to track the fatigue crack tip with respect to local coordinate systems established on the specimen surface. A grid is drawn and subdivided into units with proposed nomenclature. Compact Tension and Shear (CTS) specimens, extracted from AA-7085 plates, undergo fatigue loading in a servo-hydraulic universal testing machine. A fixture proposed by Richard et al. induces planar mixed-mode loading cases in the specimen. During experiments, the digital microscope tracks the crack tip using grid unit corners as local origins. The local coordinates of the crack tip are transformed into the crack tip coordinates with respect to the pre-crack tip. Crack evolution data are used to determine the fatigue crack growth rate by analyzing tangents of a three-parameter fitted curve. The equivalent SIF ranges are computed at different crack lengths in an XFEM script written in Ansys. The modified Paris parameters are found and experimentally observed crack deflection angles are compared with the Maximum Tangential stress, Strain energy density, and Richard’s criterion.

Exploiting fractal features to determine fatigue crack growth rates of metallic materials

An alternative approach to the classical fracture mechanics equation to quantify the fatigue crack growth rate is proposed and examined. The method exploits the fractal features of the propagating fatigue crack. The reference crack growth response of AISI 410 martensitic stainless steel is established using compact tension C(T) specimens. Fractal analysis of microscopic images along the edge length of the crack establishes the fractal dimensions, dF of the fatigue crack. The box-counting algorithm is developed for the fractal analysis based on optical images of the crack at 100X magnification and the resolution of 1090 pixels/mm. Results show that the crack initially exhibits a Euclidean nature (dF ≈ 1). The fractal dimension increases steadily with increasing crack length in the Paris crack growth rate region with 1.05 < dF < 1.24. The corresponding stress intensity factor range varies between 18 ≤ ΔKI ≤ 40 MPa√m. The fractal dimension, dF correlates linearly with the normalized stress intensity factor range, ΔKKIC within the Paris crack growth region. This enables the multifractal fatigue crack growth rate equation to be established in terms of the fractal dimension, Paris coefficient and exponent, and fatigue fracture properties of the material. The fatigue crack growth rate of the material could then be determined using the multifractal fatigue crack growth rate model without requiring the geometry factor of the crack.

Stress intensity factor and T-stress solutions for three-dimensional clamped single edge notched tension (SENT) specimens

In the present paper, a crack compliance analysis approach and extensive three-dimensional finite element analysis were conducted for clamped SENT specimens, which is one of the most widely used low-constraint specimens for less-conservative fracture toughness testing. A wide range of geometrical parameters variations are considered including in-plane crack depth to plate width ratio (a/W), out-of-plane plate thickness to width ratio (B/W), and daylight to width ratio (H/W). Complete solutions of stress intensity factor (K), in-plane T-stress (T11) and out-of-plane T-stress (T33) are obtained. The results obtained from above two methods are in good agreement. Furthermore, the combination of the effects of crack depths (a/W), plate thickness (B/W), and daylight to width ratio (H/W) on the stress intensity factor, T11 and T33 stress are thus illustrated. To better understand the difference between the derived stress intensity factor solutions and 2D plane strain results, fracture experiments were conducted for clamped SENT specimens with different crack depths. Solutions obtained will be very useful for analyzing fracture toughness test data and determining fatigue crack growth rate for clamped SENT specimens with different crack depths (a/W), plate thickness (B/W), and daylight to width ratio (H/W).

An experimental-finite element method based on beach marks to determine fatigue crack growth rate in thick plates with varying stress states

The relation between the fatigue crack growth rate and stress state is significant for fatigue life estimation, especially for thick-welded structures with complex stress states. This paper proposes a hybrid Experimental-Finite Element Method aimed to obtain the fatigue crack growth rate corresponding to plane stress and plane strain states. A static load marking method is proposed to mark a series of crack fronts in a single edge notched bending specimen at known numbers of cycles, which is analysed by nonlinear finite element method to evaluate the stress state by a local constraint factor. Stress intensity factor at the center of the thickness and the surface position where plane strain and plane stress states approximately exist and remain unchanged with crack propagation, is calculated by the 1/4-node displacement method with consideration of non-orthogonal mesh influence. The J-integral method and the virtual crack closure technique are also applied to check the performance of the methods in dealing with the actual cracked body problem. Crack length increments are determined based on the crack front profiles. The da/dN-ΔK curves of plane strain and plane stress states are determined and compared with the results from normal fatigue crack growth rate tests according to Chinese standard: GB/T 6398-2000. The fatigue crack growth behavior of a semi-elliptical surface crack located at the weld toe of a T-plate welded joint subjected to cyclic tension loading is assessed based on the curves and the analytical results are compared with the experimental results. The asymptotic crack shape observed in experiments is successfully predicted by using the curves determined by the hybrid method.

Mode I fatigue delamination growth with fibre bridging in multidirectional composite laminates

Fatigue delamination in multidirectional composite laminates was experimentally investigated in present study. Both the Paris relation and a modified Paris relation (with a new similitude parameter) were employed to interpret fatigue delamination with significant fibre bridging. The results clearly demonstrated that fatigue delamination was independent of fibre bridging, if a reasonable similitude parameter was used in data reduction. As a result, a master resistance curve can be fitted to determine fatigue crack growth with different amounts of fibre bridging. The energy principles were subsequently used to provide physical interpretation on fatigue delamination. The results indicated the energy release for the same fatigue crack growth remained constant with fibre bridging. Bridging fibres in most cases just periodically stored and released strain energy under fatigue loading, but had little contribution to real energy release. The master resistance curve was finally applied to predict fatigue delamination with fibre bridging. Acceptable agreement between predictions and experiments was achieved, demonstrating the validation of the modified Paris relation in fibre-bridged fatigue delamination study.

A validation of a modified Paris relation for fatigue delamination growth in unidirectional composite laminates

Abstract The aim of this paper is to provide evidence on the validation of a modified Paris relation in fatigue crack growth with fibre bridging. Energy principles were first applied to investigate energy release in fatigue delamination growth. A comparison between the Paris and the modified Paris relations was completed subsequently. The application of the Paris relation can artificially cause different resistance curves of fatigue delamination with fibre bridging, violating the hypothesis of similitude and the energy dissipation results. However, the use of the modified Paris relation can result in a master resistance curve, which is physically consistent with the law of similitude and the energy release regulations. This derives from using an appropriate similitude parameter in data reduction. It is therefore reasonable to use the strain energy release rate (SERR) actually applied on the crack front, rather than the total applied SERR, as similitude to correlate fatigue crack growth. The master resistance curve was finally employed to predict fatigue results from literature. Acceptable agreement between predictions and experiments was achieved, validating the effectiveness of the modified Paris relation in determining fatigue crack growth with fibre bridging.

Fibre bridging effect on the Paris relation of mode I fatigue delamination in composite laminates with different thicknesses

Fatigue delamination with fibre bridging in composite laminates with different thicknesses was investigated. The experimental results clearly demonstrated fibre bridging had significant retardation effects on fatigue delamination behavior, making it insufficient to use a single Paris resistance curve to determine fatigue crack growth. To address this problem, the coefficients of the Paris relation were correlated to the normalized crack extension (a−a0)/Lpz. It was found that the exponent n was independent on the normalized crack extension and specimen thickness, whereas the parameter log(c) bi-linearly decreased with the normalized crack extension and kept constant once fibre bridging became saturation. And the magnitude of log(c) was independent on specimen thickness. Thus, it was concluded that fatigue delamination behavior and fibre bridging significance were independent on specimen thickness at a given normalized crack extension (a−a0)/Lpz. With substitutions of these correlations into the Paris relation, an empirical power law relation was developed to characterize fatigue delamination behavior. And its validation was verified by a comparison between predictions and experiments.

Corrosion Fatigue Tests Using Strain Gauges for Measuring Load and Crack Length

This paper uses numerical analysis and experimental data to validate the use of strain gauges for load and crack propagation measurements in corrosion fatigue. It was shown that the measurement of crack length and load by strain gauges can be done following the requirements of ASTM E647-15. The results open the possibility for using strain gauges directly positioned on the samples, replacing both the classical load cells to measure load and direct current potential drop to determine fatigue crack growth rate, as neither are easily usable for high-pressure corrosion fatigue tests.

Fibre bridging effect on the Paris relation for mode I fatigue delamination growth in composites with consideration of interface configuration

Fibre bridging can significantly enhance delamination resistance making the use of a single Paris resistance curve to determine fatigue crack growth insufficient. An empirical Paris-type relation has been developed in a previous study to take fibre bridging into account in fatigue delamination growth. This relation was developed by correlating the Paris constants C and n to the amount of fibre bridging. This paper provides a further investigation on the interface configuration effect on fatigue delamination growth, illustrating the significance of fibre bridging. The results demonstrated that more bridging fibres can be generated in a multidirectional interface, making both log(C) and n significantly depend on fibre bridging. Thus, the method proposed in the previous study is further extended to take into account of the interface configuration effect.

Effect of fibre volume fraction and fibre direction on crack paths in flax fibre-reinforced composites

Mechanical and fracture mechanical behaviour of composites reinforced with unidirectionally aligned flax fibres is investigated experimentally and numerically. Thereby, the main points are the determination of crack paths in compact tension specimens with three different fibre directions under static as well as fatigue loading and their fatigue crack growth rate curves. Due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but affected by the fibre direction and fibre volume fraction as well. Therefore, the well-known stress intensity factor solutions for the standard specimens are not applicable. Consequently, extensive numerical simulations have been carried out to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. An approach for calculating stress intensity factors analytically with geometry correction factor functions is conducted exemplified for one fibre direction.

Investigation of crack paths in natural fibre-reinforced composites

Nowadays, fibre-reinforced composite materials are widely used in many fields, e.g. automotive and aerospace. Natural fibres such as flax and hemp provide good density specific mechanical properties. Additionally, the embodied production energy in natural fibres is much smaller than in synthetic ones. Within this paper the fracture mechanical behaviour of flax fibre-reinforced composites is discussed. Especially, this paper focuses on the determination and investigation of crack paths in compact tension specimens with three different fibre directions under a static as well as fatigue load. Differences and similarities in the obtained crack paths under different loading conditions are presented. Due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but practically determined by the fibre direction and fibre volume fraction. Therefore, the well-known stress intensity factor solutions for the standard specimens are not applicable. It is necessary to carry out extensive numerical simulations to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. Those numerical crack growth simulations are performed with the three-dimensional crack simulation program ADAPCRACK3D to gain energy release rates and in addition stress intensity factors.

Setup for evaluation of fatigue crack growth in rubber: Pure shear sample geometries tested in tension-compression mode

A novel measurement setup is developed to determine fatigue crack growth and heat build-up in rubber. Loading conditions include tensile and compressional loads. Deviations in the crack shape are detected with special features (swivel arm and additional light sources) and provide the possibility of a subsequent manual correction of the shadow crack length. This results in improved reproducibility and a worst-case scenario is obtained.Flat pure shear (PS) samples with 2 mm and 4 mm thickness are compared with faint waist pure shear (FWPS) samples. Especially due to the waisted shape and the corresponding non-uniform strain distribution, FWPS samples show augmented in-plane crack growth, but the validity of the tearing energy concept is questionable. PS samples with 4 mm thickness can easily support compressional loads but they show larger heat build-up at comparable tearing energies due to increased thickness. Thus, advantages and disadvantages are identified for each geometry.

Numerical Modelling of Crack Growth in a Gear Tooth Root

A computational model for determination of crack growth in a gear tooth root is presented. Two loading conditions are taken into account: (i) normal pulsating force acting at the highest point of the single tooth contact and (ii) the moving load along the tooth flank. In numerical analysis it is assumed that the crack is initiated at the point of the largest stresses in a gear tooth root. The simple Paris equation is then used for a further simulation of the fatigue crack growth. The functional relationship between the the stress intensity factor and crack length K = f(a), which is needed for determining the required number of loading cycles N for a crack propagation from the initial to the critical length, is obtained using a displacement correlation method in the framework of the FEM-method considering the effect of crack closure. The model is used for determining fatigue crack growth in a real gear made from case carburised and ground steel 14CiNiMo13-4, where the required material parameters were determined previously by appropriate test specimens. The results of the numerical analysis show that the prediction of crack propagation live and crack path in a gear tooth root are significantly different for both loading conditions considered.

Effect of steady torsion on fatigue crack initiation and propagation under rotating bending: Multiaxial fatigue and mixed-mode cracking

Abstract Axles and shafts are of prime importance concerning safety in transportation industry and railway in particular. Knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is therefore essential for design and maintenance purposes. The effect of a steady torsion on both small and long crack growth under rotating bending is focused in this paper. For small crack growth, a modified effective strain-based intensity factor range is proposed as the parameter that correlates small fatigue crack growth data under proportional or non-proportional multiaxial loading conditions. Results show that this parameter is appropriate for determining fatigue crack growth of small cracks on rotating bending with an imposed steady torsion.

Flight-by-flight fatigue crack growth life assessment

Conventionally, fatigue crack growth in aircraft structures under flight spectrum loading is often analysed and predicted based on crack growth rates obtained from constant-amplitude crack growth testing with cycle-by-cycle life prediction methods or models. Because the mechanism of fatigue crack growth under spectrum loading is yet to be fully understood, no matter how closely the models are able to account for the load interaction effects, the predictions generally have to be subjected to the validation by fatigue crack growth tests using either representative specimens or real structures under the representative flight spectrum. In view of this fact, it is not difficult to deduce that the predictions should be much more reliable if the predictions are made directly based on the flight spectrum crack growth data. Therefore, a new approach to fatigue crack growth life assessment has been proposed in this paper based on the analysis of flight-by-flight fatigue crack growth data measured by quantitative fractography for several common aircraft structural materials under various fighter aircraft flight spectra. Quantitative fractography was successfully used for titanium coupons to generate crack growth curves under flight spectrum loading. The crack growths were also shown to be exponential. As a demonstration, the flight-by-flight approach was used to determine fatigue crack growth lives of aircraft aft fuselage frames under a fighter aircraft usage.

New testing procedure to determine da/dN–ΔK curves at different, constant R-values using one single specimen

A new concept for fatigue crack propagation tests has been developed. Using a single specimen, it is possible to determine fatigue crack growth curves (da/dN–ΔK) for every stress ratio between R=0.9 and R=−1. Additionally, the new concept also provides threshold values for fatigue crack growth for different values of R. In combination with a continuous, autonomous crack length measurement tool (such as the DC potential drop method) this testing procedure can be implemented with minimal time and effort. The test procedure consists of a sequence of Kmax-constant tests with decreasing crack growth rates. There should be no load history effects. According to the procedures described in the ASTM Standard E 647, the results using this new testing procedure fit very well to the da/dN–ΔK curves generated with different specimens. The tests also fulfil all the requirements of ASTM Standard E 647.

Transverse fatigue crack propagation behavior in equine cortical bone

Stress fractures stem from the initiation and propagation of fatigue cracks through bone, and fatigue damage may play a role in many other orthopaedic problems, such as hip fractures in the elderly. The objective of this investigation was to measure fatigue crack propagation rates in cortical bone. Specific aims were to determine fatigue crack growth rate, da/dN, as a function of alternating stress intensity factor, ΔK, for equine third metacarpal cortical bone tissue; to determine whether the resulting data followed the Paris law; and to test the hypothesis that crack growth rates differ between dorsal and lateral regions. Compact type specimens oriented for transverse crack growth were subjected to fatigue under Mode I loading. The da/dN vs. ΔK data for the dorsal specimens revealed a Paris law exponent of 10.4 (R2 = 0.82), comparable to that for ceramics. These data also exhibited an apparent threshold stress intensity factor of 2.0 MPa · m1/2. It was not possible to obtain similar results for lateral specimens because all cracks deviated from the desired transverse path and ran longitudinally in spite of the use of side grooves to constrain the crack path. However, the results for lateral specimens were not due to a failure of the test method, but reflect dramatic differences in fatigue crack propagation resistance between the two cortical regions. These results are consistent with clinical observations that stress fractures in the third metacarpus typically occur in the mid-diaphysis of the dorsal cortex, but not in the lateral cortex.

A technique to measure fatigue crack growth threshold

An experimental technique for determining fatigue crack growth threshold is presented. This experimental technique uses an increasing ΔK step loading procedure to determine threshold going from a no-growth to growth status. Stress relief annealing of the Ti-6AI-4V test specimens eliminates load history effects normally associated with the precrack, providing a measurement equivalent to what is achieved by a standard ASTM load shed test. In addition to measuring load history free thresholds, this increasing ΔK technique can be used to investigate different load history effects on threshold by using the threshold step measurement with different precrack histories and without the subsequent annealing process. Verification of the threshold step measurement is demonstrated by comparing measurements with standard ATSM load shed testing results.

Fracture resistance and fatigue crack growth characteristics of two AlCuMgZr alloys

The dependence of strength, fracture resistance, and fatigue crack growth rate on the aging conditions of two alloy compositions based on Al-3.7Cu-1.85Mg-0.2Mn is investigated. Mechanical properties were evaluated in two heat treatment conditions and in two orientations (longitudinal and transverse). Compact tension specimens were used to determine fatigue crack growth characteristics and fracture resistance. The aging response was monitored on coupons using hardness measurements determined with a standard Rockwell hardness tester. Fracture resistance is found to increase with increasing yield strength during artificial aging of age-hardenable 2124-Zr alloys processed by powder metallurgy techniques. Fatigue crack growth rate increases with increasing strength. It is argued that these changes are related to deformation modes of the alloys; a homogeneous deformation mode tends to increase fracture resistance and to decrease the resistance to the fatigue crack propagation rate.

Cumulative-damage modeling of fatigue crack growth in turbine engine materials

Life predictions of turbine engine structural components utilize fracture mechanics principles to determine fatigue crack growth rates. Fatigue cracks grow under conditions of variable temperature, frequency, hold time, stress ratio and stress level. At elevated temperatures, time-dependent material behavior can play a significant role in the material behavior. Cumulative-damage models must account for all these variables as well as interaction effects. The earliest modeling involved interaction schemes and, primarily, time-independent material behavior. More recent work has focused on time-dependence and creep-fatigue interaction effects. A review of current modeling concepts is presented.