Fatigue crack growth of PMMA in organic agents

Crack growth tests under cyclic loading were executed at 295 K in various organic agents using compact tension and pure bending specimens of polymethylmethacrylate (PMMA). The cyclic frequencies f for the two kinds of test were 0.4 to 1 and 33 Hz, respectively. Two interesting features are pointed out: (i) transitional behaviour is observed on a crack growth rate against stress intensity factor range K diagram, and (ii) the fatigue fracture surfaces tested in highly viscous agents are covered with a new type of striation named wavy striation, as reported previously. The crack growth rate at the transition was analysed based on fluid flow through the pores within the craze forming at the crack tip. The wavy striation was also investigated by use of the theory of meniscus instability. It is found that both the phenomena may be well described by a parameter P = T(K) ²/f where T and are the surface tension and viscosity of the organic agents, respectively.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Fatigue crack growth retardation under constant amplitude and variable mean stress

Fatigue crack growth retardation under stress spectra with constant amplitude and variable mean stress, respectively, was studied. Flat specimens with a central through crack were tested under tension-tension load. The specimens were made with low alloy steel 4 mm thick, with yield strength of 625 Mpa and ultimate tensile strength of 784 MPa. Overload affected crack length increments Δa¹ were studied. The best correlation was obtained between monotonic plane stress plastic zone size 2r_y and Δa¹. The cyclic plastic zone size 2r_pc correlated with crack length increment of minimum crack growth rate after overload. Forman's equation and Willenborg's model of fatigue crack growth retardation were used for theoretical prediction of fatigue crack propagation life. The best agreement between theoretical and experimental results was also obtained using monotonic plastic zone size instead of monotonic plastic zone radius or cyclic plastic zone size. The agreement is reasonably good, even though in the case of one spectrum, cracks were arrested for several thousand cycles.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Fatigue crack propagation under variable amplitude loading in PMMA and bone cement

Fatigue failure of PMMA bone cement is an important factor in the failure of cemented joint replacements. Although these devices experience widely varying loads within the body, there has been little or no study of the effects of variable amplitude loading (VAL) on fatigue damage development. Fatigue crack propagation tests were undertaken using CT specimens made from pure PMMA and Palacos R bone cement. In PMMA, constant amplitude loading tests were carried out at R- ratios ranging from 0.1 to 0.9, and VAL tests at R = 0.1 with 30% overloads every 100 cycles. Palacos R specimens were tested with and without overloads every 100 cycles and with a simplified load spectrum representing daily activities. The R- ratio had a pronounced effect on crack propagation in PMMA consistent with the effects of slow crack growth under constant load. Single overloads caused pronounced crack retardation, especially at low da/dN. In Palacos R, similar overloads had little effect, whilst individual overloads at low da/dN caused pronounced acceleration and spectrum loading retarded crack growth relative to Paris Law predictions. These results demonstrate that VAL can have dramatic effects on crack growth, which should be considered when testing bone cements.     

Fatigue crack paths for inclined cracks and surface flaws under biaxial loading

Two approaches are developed for geometrical modeling of crack growth trajectories for the inclined through thickness central cracks and the part-through surface flaw respectively. The principal feature of such modeling is the determination of crack growth direction and the definition of crack length increment in this direction. The damage process zone size concept is employed for calculations of mixed-mode crack growth trajectories and surface flaw shape and positions. Crack front behavior for a straight-fronted edge crack in an elastic bar of circular cross-section is studied through experiments and computations under axial tension loading. The elaborated theoretical model is applied for fatigue crack shape simulation of part-through cracks in a hollow thick- and thin-walled cylinders under different biaxial loading conditions. Suggested approach of crack paths modeling is used for an analysis and prevention of operation failures of existing in-service aircraft gas-turbine engine rotating components.     

Fatigue crack propagation under cyclic thermal stress

Structures used at elevated temperature subject to severe cyclic thermal stress. Therefore, accurate prediction procedures for thermal fatigue crack growth should be applied to rationalise component flaw assessment. Fatigue crack propagation tests under thermal stress were carried out using an modified type 316 stainless steel (316FR), which is a candidate material for the fast reactor in Japan. Thermal stress of the tests was generated by cyclically changed temperature distribution through thickness in a plate by induction heating and air-cooling. Numerical analysis was also carried out to examine the applicability of the J integral under cyclic thermal stress. The J integral under elasto-plastic condition under thermal stress is close to the elastically calculated J integral. Prediction by J integral tends to be conservative for deeper cracks, and modification of the J integral value using crack opening ratio gives good agreement with the experimental crack growth.     

Fatigue crack growth retardation in plane stress and plane strain

The fatigue crack growth retardation phenomenon following a single peak overload applied tothick andthin SEN bend specimens has been studied for a low carbon structural steel. Fatigue tests were performed under a constant load ratio of 0.6, constant stress intensity range of 10 MPam^1/2 and a constant overload ratio of 2.5. An immediate increase followed by a transient retardation in the fatigue crack growth rate, due to the applied overload, was observed for thethick specimen but complete crack arrest was obtained for thethin specimen. The immediate increase in the fatigue crack growth rate following the single peak overload in thethick specimen was attributed to the coincidence of monotonic fracture modes.     

Fatigue crack growth in TRIP steel under positive R-ratios

Load-controlled fatigue tests are conducted for four positive R values on a low-alloy TRIP steel for two different heat treatments: an optimal treatment leading to a multiphase microstructure containing retained austenite, ferrite, bainite and martensite, and a non-optimal treatment leading to a ferritic–martensitic dual-phase microstructure. A significantly increased resistance to fatigue crack growth is found for the optimal case with respect to the non-optimal case. The amount of crack closure is found to be larger in case of the non-optimally treated (ferritic–martensitic) steel. Close to the crack tip, an increased hardness suggests martensite formation. An EBSD technique is used to quantify the volume of retained austenite ahead of the crack tip, within the plastic zone. It is found that martensite formation only occurs within the monotonic plastic zone during fatigue. By evaluation of the retained austenite fraction during straining in static tensile tests, the plastic strain levels within the plastic zone are assessed. Additionally, the effect of martensite formation on fracture toughness is estimated.     

Fatigue crack growth of polycarbonate under high pressures

In order to investigate the effect of hydrostatic pressure on the fatigue crack growth behaviour of solid polymers, an apparatus was designed for maximum pressure of 3000 kgf cm^–2. The crack growth rates as a function of stress intensity factor range, K, were measured using compact tension specimens of polycarbonate under pressures of 1–2000 kgf cm^–2. It was shown that (1) the fatigue crack growth rates at pressures higher than 500 kg cm^–2 were nearly insensitive to hydrostatic pressure, (2) the slope on a log (dc/dN) versus log (K) diagram was higher at the high pressures than at an atmospheric pressure, and (3) shear lips and the tear lines appeared on the fracture surfaces at atmospheric pressure, while they were not observed at pressures higher than 500 kgf cm^–2.     

The inclined crack under biaxial load

The problem of a sheet with an inclined crack subject to a system of biaxial loads is examined in a manner similar to that used in our previous publications. The combined effect of load biaxiality and crack orientation on $\text{K}{}_{\mathrm{l}}$, $\text{K}{}_{\mathrm{II}}$, maximum shear, anile of initial crack extension, elastic strain energy density, as well as on the local strain energy rate is made explicit. Once again it is shown that use of the so-called “singular solution” for expression of the local crack-tip elastic stress and displacements is not sufficient to give adequate account of the biaxial load effect.