Study of Fatigue Behavior of Epoxy‐Carbon Composites under Mixed Mode I/II Loading

This paper presents an experimental assessment of the initiation and propagation of interlaminar cracks under mixed mode I/II dynamic fracture loading of a composite material with an MTM45‐1 epoxy matrix and unidirectional IM7 carbon‐fiber reinforcement. The aims of the experimental program developed for this purpose are to determine, on the one hand, the initiation curves of the fatigue delamination process, understood as the number of load cycles needed to generate a fatigue crack, and on the other, the crack growth rate (delamination rate) for different percentages of static Gc, in both cases for two mode mixities (0.2 and 0.4) and for a tensile ratio R = 0.1. All this with the goal of quantifying the influence of the degree of mode mixity on the overall behavior of the laminate under fatigue loading. The results show that the energy release rate increases with increasing loading levels for both degrees of mode mixity and that the fatigue limit is located around the same percentages. However, crack growth rate behavior differs from one degree of mode mixity to the other. This difference in the behavior of the material may be due to the varying influence of mode I loading on the delamination process.

     

Eigenspannungen als Parameter des röntgenographischen Bruchkriteriums und der Lebensdauervoraussage

Residual stresses as parameters of X-ray criterion of fracture and of fatigue life prediction Fatigue testing is notorious for considerable scatter in specimen life even if special measures are taken to precisely control parameters of stress cycling. The reason for that must be ascribed to variation in material microstructure existing prior to fatigue loading. Structural condition of material may be determined by the following function: Extensive fatigue tests on α-Ti and (α + β)-Ti alloy at temperatures 77 K and 295 K showed that failure did not occur until function V reached its critical value at a plane characteristic of each lattice type (failure plane). The condition V = K may be therefore regarded an X-Ray criterion and, once determined numerically, a sort of material constant. The life N_B of fatigue tested specimen was found to be clearly depended on structural condition of virgin material exhibited natural variation of structural characteristics. The finite fatigue life was found to conform with the relationship The expression may be used for predicting life N_B if prior to fatigue loading the material condition function V value is made known for a characteristic lattice plane.     

Torsionswechselversuch mit kaltpreßgeschweißten Zirkonium/Stahl-Proben

Torsional cycling of cold pressure welded zirconium/steel-specimens . Low-cycle fatigue of cold pressure welder zirconium/steel-specimens has been studied in cyclic torsion. The critical number of cycles N_cr instead of the number of cycles to final failure N_f is taken for evaluation of the endurance life in low-cycle fatigue. N_cr is defined as the number of cycles leading to the formation of a crack which noticeably weakens the specimen. The relationship N · Δγ = const. is achieved for bonded specimens. The results have been correlated with the observations in unwelded zirconium and steel to predict the endurance life of bonded specimens. Microstructure studies revealed crack initiation at points of intense slip in zirconium. Fracture occured always in zirconium outside the welded zone.     

Path prediction of I + III mixed mode fatigue crack propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the propagation rate expression and the path prediction. It is found that during the mode transformation process, the crack propagation rate is still controlled by the mode I stress intensity factor; and Paris equation also holds for the relationship between and ΔK_I . Crack propagation path can be predicted only when both the crack mode transformation rate and propagation rate are available.     

Change of fatigue parameters with temperature

A fatigue crack growth rate (FCGR) equation, had been proposed which predicts the observed R-ratio effects correctly. Conceptually, this equation accounts for spectrum loading effects via the parameter “K”. The work presented deals with the temperature effect on the fatigue parameters entering the above FCGR-equation. For materials which do not experience a microstructural or a fracture mode transition within the temperature range of interest, the effect of temperature on the fatigue parameters “C” and “ΔK^T” can be interpolated or extrapolated from relatively few experimental data. Extrapolation of these fatigue parameters for Inconel X-750 measured between 300° K and 900° K allowed a very accurate prediction of the FCGR at 4° K. At higher temperatures the end of fatigue controlled crack growth is clearly indicated by a rapid increase of the fatigue parameter “C”. There, the fatigue parameter “C” increases withing a temperature span of 100° K by a factor of 10². This kind of information is of utmost importance for materials application at elevated temperatures as in nuclear systems.     

Transformation zones, crack shielding, and crack-growth resistance of Ce-TZP/alumina composite in mode II and combined mode II and mode I loading

Crack-tip transformation zones, crack shielding and crack-growth-resistance (R-curve) behaviors of a transformation-toughened ceria-partially stabilized zirconia–alumina (Ce-TZP/alumina) composite were studied in mode II and combined mode I and mode II loading using compact-tension-shear (CTS) specimens. The mode II and mode I stress intensities for both the initial straight cracks and the subsequent kinked cracks were assessed by the method of caustics using geometrically equivalent specimens of polymethyl methacrylate (PMMA). The angle of formation of the transformation zones as well as of extension of the cracks increased systematically with increasing ratio of the mode II and the mode I stress intensities and approached a value of θ^*=−72° in pure mode II loading. This angle was close to the angle for maximum hoop tension in the stress field of a mode II crack (θ^*=−70.5°). A crack-initiation toughness envelope was constructed on a K_I–K_II diagram using the critical loads for incremental crack extension. The crack-initiation toughness in pure mode II loading was less than the corresponding toughness in mode I loading. This result was consistent with calculations that indicated no shielding from the asymmetric and elongated zones developed in mode II loading. The fracture toughness measured for the kinked cracks at long kink lengths approached the maximum fracture toughness measured for a mode I crack.     

Three-dimensional crack analysis using singular boundary elements

A multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The displacement and traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.     

Modes of dynamic shear failure in solids

The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

On Oxygen Diffusion in tetragonal zirconia

Oxygen diffusion in dense scales of tetragonal zirconia at 1100–1300°C has been studied by the so-called interruption kinetic method (or the Rosenberg method). Assuming that oxygen vacancies are the predominant defects in zirconia (ZrO₂), studies by this method provide values of the oxygen self diffusion coefficient in this oxide at its lower limit of stability, D, and the value in tetragonal zirconia can be expressed as D =2.2 · 10^?3 exp (?140(kJ/mole)/RT). The studies furthermore show that the maximum non-stoichiometry in tetragonal zirconia, X in ZrO_2?x, is small and has a value about x* ～ 0.03 at 1000–1300°C.     

EARLY DEVELOPMENT OF FATIGUE CRACKING AT MANUAL FILLET WELDS

Abstract— An experimental study within the Canadian Offshore Corrosion Fatigue Research Programme was performed on the early development of fatigue cracking along the wavy toe of manual fillet welds between structural steel plates. Stress relieved and as-welded cruciform joints were tested under R = −1 and R = 0 loading at different stress amplitudes. The depth and the opening level of cracks as small as 10–20 μm were monitored using miniature strain gauges installed along the toe apex, in combination with beach marking. Most of the "initiation life" (25% to 50% of total life), conventionally defined by a crack depth of 0.5 mm, is consumed in short crack propagation. Three types of short crack development for different combinations of local mean stress and stress range are identified and analyzed. Growth rates in as-welded specimens are faster than in stress relieved specimens, which results in shorter "initiation lives". This is associated with a higher effective stress range, particularly under R = - 1 loading where cracks are open over nearly the full stress range. The V-notch stress intensity factor is a promising parameter to rationalize the crack "initiation life". It takes into account the thickness effect experimentally observed. Under R = - 1 loading of as-welded joints, using R = 0 data and taking the whole stress range gives a reasonably conservative approximation of the crack "initiation life".     

A REVIEW OF FATIGUE CRACK GROWTH IN STEELS UNDER MIXED MODE I AND II LOADING

The majority of methods for predicting the direction of propagation of mixed mode cracks have assumed that they branch to grow as mode I cracks. However, under some circumstances mode II crack growth occurs. Rolling contact fatigue cracks are one example of an industrial problem where cracks appear to grow under predominantly mode II loading without branching. This paper reviews the available models and the experimental studies in the literature on mixed mode I and II loading, and discusses the parameters that affect the mode of crack growth.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

Failure modes and fatigue life estimations of spot friction welds in cross-tension specimens of aluminum 6061-T6 sheets

Failure modes of spot friction welds (SFWs) in cross-tension specimens of aluminum 6061-T6 sheets are investigated. Micrographs of the SFWs before and after failure under quasi-static and cyclic loading conditions are examined. Two different nugget pullout failure modes can be seen. A fatigue crack growth model based on the paths of the dominant kinked fatigue cracks is adopted to estimate the fatigue lives of SFWs. The computational stress intensity factors for finite kinked cracks and the Paris law for fatigue crack propagation are considered. The fatigue life estimations based on this model agree well with the experimental results.     

Interlaminar fatigue crack growth of cross-ply composites under thermal cycles

The fatigue growth of a fiber reinforced composite laminate was characterized under thermal cycling using a combined experimental and computational investigation. Twenty-four ply composite laminates ([0°₁₂/90°₁₂]) are fabricated with a pre-existing delamination, and subjected to thermal cycling in an environmental chamber. The large mismatch in the coefficients of thermal expansion is used to grow an interlaminar crack at the interface of the 0° and 90° laminae. This thermal fatigue crack growth behavior is investigated for different amplitudes of temperature change (ΔT = 30–140 °C). The inspection of fracture surfaces, after completion of the fatigue tests, reveals an angled or kinked crack front growth with greater propagation distances near the free-surfaces/edges. Due to the non-uniform crack growth across the specimen thickness, three-dimensional finite element analyses are performed to investigate the fatigue growth mechanisms under thermal load. From the analysis, the energy release rate as well as the mixed-mode stress intensity factors is calculated and the variations of these fracture parameters are found to be consistent with the observed crack front configuration. Using the computed results, the experimentally measured crack growth rates are also correlated with the amplitude of energy release rate, and a power law form of the fatigue law is established. The relevant coefficients as well as the threshold energy release rate are also determined. The present analysis is useful for not only understanding the fatigue delamination mechanisms under thermal cycling but also for estimating the threshold temperature variation that is needed to drive crack growth.     

SHEAR FATIGUE CRACK GROWTH: A LITERATURE SURVEY

A fatigue crack is often initiated by a localized cyclic plastic deformation in a crystal where the active slip plane coincides with the plane of maximum shear stress. Once a crack is initiated, the crack will propagate on the maximum shear plane for a while and, in the majority of the cases, will eventually change to the plane of the applied tensile stress. The “shear” and “tensile” modes of fatigue crack propagation are termed stage I and stage II fatigue crack growth. They are also known as mode II and mode I fatigue crack growth. However, the mechanism of the tensile mode fatigue crack propagation is shear in nature. Considerable progress has been made recently in the understanding of mode II fatigue crack growth. This paper reviews the various test methods and related data analyses. The combined mode I and mode II elastic crack tip stress field is reviewed. The development and the design of the compact shear specimen are described and the results of fatigue crack growth tests using the compact shear specimens are reviewed. The fatigue crack growth tests and the results of inclined cracks in tensile panels, center cracks in plates under biaxial loading, cracked beam specimens with combined bending and shear loading, center cracked panels and the double edge cracked plates under cyclic shear loading are reviewed and analyzed in detail.     

Vorhersagemodell für die Wachstumsraten kurzer Risse auf der Basis von Kmax‐konstant‐Versuchen an M(T)‐Proben

Prediction model for the growth rates of short cracks based on K_max‐constant tests with M(T) specimens The fatigue crack growth behaviour of short corner cracks in the Aluminium alloys Al 6013‐T6 and Al 2524‐T351 was investigated. The aim was to determine the crack growth rates of small corner cracks at stress ratios of R = 0.1, R = 0.7 and R = 0.8 and to develop a method to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T)‐specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The pre‐cracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a Focussed Ion Beam. The results of the fatigue crack growth tests with short corner cracks were compared with long fatigue crack growth test data. The short cracks grew at ΔK‐values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK‐values and the same stress ratios. A model was developed on the basis of K_max‐constant tests with long cracks that gives a good and conservative prediction of the short crack growth rates.     

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, K, 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. K data for the dorsal specimens revealed a Paris law exponent of 10.4 (R ² = 0.82), comparable to that for ceramics. These data also exhibited an apparent threshold stress intensity factor of 2.0 MPa · m^1/2. 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.     

Multiaxial fatigue behaviour of A356‐T6

Aluminum alloy A356‐T6 was subjected to fully reversed cyclic loading under tension, torsion and combined loading. Results indicate that endurance limits are governed by maximum principal stress. Fractography demonstrates long shear mode III propagation with multiple initiation sites under torsion. Under other loadings, fracture surfaces show unique initiation sites coincidental to defects and mode I crack propagation. Using the replica technique, it has been shown that the initiation life is negligible for fatigue lives close to 10⁶ cycles for combined loading. The natural crack growth rate has also been shown to be comparable to long cracks in similar materials.