Mechanics of crack growth in epoxide resins

Experiments have been conducted employing tapereddouble-cantilever-beam joints with different epoxide adhesives. Depending on the adhesive employed, crack propagation occurred either (a) in a continuous stable manner with crack propagation velocities in the range 10^?4 to 5 m/s and values of the adhesive fracture energy, G_Ic, being almost independent of the crack velocity, or (b) intermittently in an unstable manner when the initial crack velocity was never less than about 20 m/s and, in some instances, rose to about 450 m/s; values of G_Ic (initiation) increased rapidly with increasing velocity. It is proposed that the amount of localized plastic deformation arising from shear yielding that occurs at the crack tip prior to crack propagation is controlling. Secondly, the longterm strength of stressed, structural adhesive joints has been investigated. The fracture of these joints over eight decades of time is uniquely described by a critical plastic zone size developed at the crack tip at failure.     

Plane strain and plane stress analysis of fatigue crack propagation in medium density polyethylene pipe materials

Using the Crack Layer Theory, differences in damage formation under different stress states during fatigue crack propagation in an ethylene-butene copolymer were quantified and compared. Despite having vastly different stress states and crack propagation behaviors, arc specimens (28 mm thick) and single edge notched (SEN) specimens (2 mm thick) were shown to have the same specific enthalpy of damage, ～300 J/g, a parameter in the Crack Layer Theory that is a measure of the material's intrinsic toughness. Damage in the SEN specimen consisted of crazing the significant material yielding; the latter damage type is associated with plane stress conditions. In the predominantly plane strain arc specimen, material yielding was minimal compared to crazing, the dominant damage form. After measuring these damage forms and applying the Crack Layer Theory, the constancy of the specific enthalpy of damage was established. Also the dissipation coefficient, β, a second parameter of the Crack Layer Theory, was shown to be a process-dependent parameter, which was inversely proportional to the lifetime of the specimen: β_SEN = 4.6 × 10^?5, β_arc = 1.1 × 10^?4, which corresponds to lifetimes of 140,000 and 30,000 cycles to failure, respectively.     

Acoustic emission behavior of epoxies during tensile loading

The acoustic emission behavior during tensile loading of two common epoxy systems of different ductility was investigated at different loading rates. At low threshold voltage, it was possible to register acoustic emissions before the final failure. Only very few emissions were recorded compared with the amount commonly recorded for metals and composite materials. The acoustic emissions detected were of burst-type, revealing a brittle damage accumulation process. They originated from the initiation and incremental growth of microcracks of stochastic nature. The events occurred before gross yielding and during the final “brittle” failure process. Basically no events were detected between gross yielding and the final failure during which large scale yielding, necking, and stable crack growth took place. The occurrence of events at the different loading rates was strongly influenced by the yielding behavior and fracture toughness, characterized by the yield stress σ_y and the plane-strain fracture toughness K_Ic respectively. K_Ic was inversely dependent on the total number of events up to gross yielding. The event distribution normalized with respect to the conditions at gross yielding was hardly affected by the loading rate.     

Fatigue crack propagation in,graphite fiber reinforced nylon 66

The rate of fatigue crack propagation in graphite fiber reinforced nylon 66 was measured. A model of the form å = β [K_max^1-γ ΔK^γ]^r was used to correlate the rate of crack propagation å with the maximum stress intensity K_max and the amplitude of the stress intensity ΔK experienced by the notched specimen during the fatigue test. The quantities β, γ and r were constant at fixed temperature and frequency of the test. It was also found that there exists both an upper and a lower threshold of stress intensity for the slow ropagation of damage during fatigue. The mechanism of crack propagation in the short graphite fiber reinforced nylon was found to be similar to the growth and fracture of crazes in thermoplastics. The propagation of damage at the crack tip is controlled by matrix deformation, cavitation, fiber breakage and fiber pullout. Damage can propagate in the absence of crack growth until a critical point is reached at which time the material fractures catastrophically.     

Crack propagation behavior and toughness of V‐notched polyethylene terephthalate injection moldings

The role of the skin and core regions in controlling the effects of V‐notches, on the fracture behavior of PET injection‐moldings, was correlated with their tensile and impact properties. Investigations revealed that there were three distinct fracture behaviors: ductile, semiductile, and brittle fracture transitions. The notch sensitivity factor for strength (K_S) in the ductile and semiductile transitions indicates that the fracture strength was not sensitive to ≤1.5 mm deep notches, which is considered the skin region. The introduction of core‐deep notches (>1.5 mm) resulted in a rapid increase in K_S. On the other hand, the notch sensitivity factor for energy (K_T) shows that the fracture energy was not sensitive at ≤0.5 mm deep notches. However, K_T increased drastically when notches >0.5 mm deep were introduced. The development of an anisotropic skin‐core structure in injection moldings is well acknowledged. This is revealed in a constant fracture behavior between 0.6 and 1.0 mm deep notches. Notably, there was a drastic change in the fracture pattern from ductile to semiductile at a critical 0.6 mm deep notch. The specimens experienced a mixed fracture behavior at 1.5 mm deep notch, which marks a transitional fracture pattern at the interface between the skin and core regions. Lastly, a constant fracture behavior was observed at notch depths ≥1.5 mm. Results show that crack opening, in the samples that had semiductile fracture, was a postnecking phenomenon. Before shear yielding, two shear lines that intersected at 45° were seen to originate from the crack root when a 1.2 kN load was applied. Conversely, crack opening and failure occurred simultaneously in brittle fractures. It is obvious that V‐notches provided a gradual transition in fracture behavior from the skin to the core regions, which confirms that the fracture behavior of PET injection moldings can be dependent on the skin and core structure. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Slow crack propagation in a heavily-filled particle reinforced epoxide resin

The fracture properties of two proprietary composite dental restorative materials and a model composite system were studied to determine the effects of filler concentration, exposure to water, and particle/polymer adhesion on subcritical crack propagation. Particle content ranged from 36 to 60 volume percent. The double torsion (DT) test was used to measure relationships between the stress intensity factor (K₁) and the speed of decelerating cracks or the rate of loading in dry and wet materials in air at laboratory conditions. Materials with weak particle/polymer interfaces fractured by continuous crack growth in both dry and wet conditions. In dry and wet materials with strong interfaces, continuous cracking also occurred at the low end of the range of speeds observed (10⁻⁷ to 10⁻³ m/s), but under test conditions of high crack speeds unstable (stick-slip) crack propagation was found in dry specimens and in wet model composites with 41 percent vol, filler. Water had a corrosive effect lowering K_1c for continuous crack propagation. The exponential dependence of K_1c on crack velocity, representing the viscoelastic response of the materials, was positively correlated to the filler concentration and the plasticizing effect of water. Observations on fracture surfaces indicate that low velocity cracks (<10⁻⁵ m/s) propagate through regions of high stress concentrations (interfaces, corners, pores) while at higher crack velocities failure occurs by a combination of interparticle and transparticle fracture.     

Fatigue crack propagation behavior of cellulose esters

The effect of plasticizer concentration on fatigue crack propagation (FCP) rate in cellulose acetate-propionate (CAP) was determined. Compact tension specimens were machined from 6.2 mm-thick injection molded plaques and tested on an MTS servohydraulic testing machine using a sinusoidal waveform with a frequency of 1 Hz. Two FCP mechanisms were identified: a crazing mechanism, which dominated at low values of stress intensity factor range, ΔK, and a shear yielding mechanism, which dominated at high values of ΔK. The value of ΔK at the onset of the transition from the crazing mechanism to the shear yielding mechanism was a function of plasticizer concentration, and therefore yield strength of the CAP. The transition in crack propagation mechanism created a V-shaped feature on the fracture surface, which could be used to weight the contributions from the two crack propagation mechanisms to the overall FCP rate.     

Universal Strain-Life Curve Exponents for Thermoplastics and Elastomers under Tension-Tension and Torsion

The fatigue behavior of 28 amorphous and semi-crystalline thermoplastic polymers and elastomers is tested under strain controlled sinusoidal tension-tension (TT) and torsion (T) at room temperature and analyzed via strain-life (total strain amplitude versus fatigue lifetime) and crack propagation rate versus total strain amplitude curves, analogous to Paris’ law. Investigating fatigue is extremely time- and resources consuming, so universal relationships between the exponents of the strain-life power-law and material properties are of high importance. For a brittle failure mechanism (I), the strain-life curves are found to have fixed exponents of B_TT,I = −0.27 and B_T,I = −0.22, respectively, while the crack propagation versus strain amplitude in TT has an exponent of m_da/dN,I = 4. For ductile failure (II), fixed strain-life curve exponents in TT of B_TT,II = −0.35 and in torsion of B_T,II = −0.48 with m_da/dN,II = 2.8 are obtained. In torsion, most semi-crystalline polymers show brittle and ductile failure depending on the applied strain amplitude, so the strain-life curve exponent changes accordingly. The universal exponents for strain-life and crack growth-strain amplitude curves offer a significant simplification to rapidly estimate, predict, and simulate the fatigue behavior of polymers.     

The effect of molecular weight on fatigue crack propagation in nylon 66 and polyacetal

The influence of molecular weight on fatigue and fracture behavior in nylon 66 (N66) and polyacetal (PA) is examined. Fatigue crack propagation (FCP) resistance and apparent fracture toughness (K_cf) in these two semicrystalline polymers increase with increasing molecular weight in a manner consistent with that reported for another semicrystalline polymer (HDPE) as well as for several amorphous polymers. The improved FCP resistance with increasing molecular weight is attributed to the development of a molecular entanglement network that more effectively resists cyclic-load-induced breakdown. A type of discontinous crack growth is identified in PA at 100Hz and in N66 (2.6% H₂O) at 50 Hz and compared with that observed in amorphous polymers.     

Fatigue behavior of neat and long glass fiber (LGF) reinforced blends of nylon 66 and isotactic PP

This paper focuses on the study of the fatigue behavior of neat and long glass fiber (LGF) reinforced nylon 66/PP-blends. The fatigue was characterized using Parislaw plots in the stable crack growth acceleration range. The fatigue crack propagation (FCP) is presented as a function of the crack growth per cycle (da/dN), the amplitude of the stress intensity factor ΔK, and of the strain energy release rate ΔG. It was also of interest to compare the order of performance found in fatigue to that in the static fracture test. The fracture surfaces were characterized with SEM to determine the failure mechanisms. Further, thermographic camera recordings were used to study the size of a “heated” area (ΔT = 2°C) that developed around the crack tip during the cyclic loading of LGF-PP with different amounts of maleic anhydride grafted PP (PP-g-MAH). For the neat materials, a different order of performance was detected under static and cyclic loading. This was explained by the different failure mechanisms observed after static and cyclic fracture that were related to different stress states of the specimens during the fracture process. On the other hand, the LGF-blends showed a similar order of performance during the static and the fatigue test. This was explained by the observation that similar fiber related failure mechanisms occurred in the composite, both after failure caused by the static and cyclic loading, respectively. For the LGF-PPs with varying PP-g-MAH content, the order of performance in fatigue did not correspond to the size of the “heated area” around the crack tip. This was caused by a change in the composite failure mechanisms, which contributed differently to the size of the “heated area” and to the fatigue performance.     

Fatigue crack propagation of rubber-toughened epoxies

Epoxies containing epoxy-terminated butadiene acrylonitrile rubber (ETBN) or amino-terminated butadiene acrylonitrile rubber (ATBN) were prepared and studied in terms of fatigue crack propagation (FCP) resistance and toughening mechanisms. Rubber incorporation improves both impact and FCP resistance, but results in slightly lower Young's modulus and T_g As T_g increases, the degree of toughening decreases. Rubber-induced shear yielding of the epoxy matrix is believed to be the dominant toughening mechanism. Decreasing fatigue resistance with increasing cyclic frequency is observed for both neat and rubber-toughened epoxies. This result may be explained by the inability of these materials to undergo possible beneficial effects of hysteretic heating. FCP resistance is linearly proportional to M_c^1/2, where M_c is the apparent molecular weight between crosslinks determined on the rubber-toughened material. FCP resistance also increases with increasing static fracture toughness K_IC. ATBN-toughened epoxies demonstrated better fatigue resistance than ETBN-toughened systems.     

Fatigue crack growth in polyethylene

Fatigue crack propagation (FCP) rates are studied in 6 mm thick specimens of high density polyethylene (HDPE) containing razor notches, Centrally-notched plates and single-edg notched bars are subjected to sinusoidal tension-compressio or tension-zero cycling at 0.5 or 2.0 Hz under load control a room temperature; crack growth is monitored using a travelling microscope. After many thousands of cycles with no observable damage at the tip of the razor notch, a craze like zone begins to form. This zone grows slowly until it reaches the length characteristic of a mature crack at the same ΔK. Crack growth proper then begins. The number of cycles to initiate crack growth falls linearly with increasing ΔK at the razor notch Subsequent crack growth is determined both by the current value of ΔK and by loading history. When ΔK is increasing, FCP rates follow a standard Paris law curve. However, reduced, FCP rates are observed following an overload.     

Fracture and impact properties of polycarbonates and MBS elastomer-modified polycarbonates

Mechanical properties of polycarbonates (PCs) and elastomer-modified polycarbonates with various molecular weights (MW) are investigated. Higher MW PCs show slightly lower density, yield stress, and modulus. The ductile–brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of PC MW and with the increase of elastomer content. The elastomer-modified PC has higher impact strength than does the unmodified counterpart if the failure is in the brittle mode, but has lower impact strength if the failure is in the ductile mode. The critical strain energy release rate (G_c) measured at ?30°C decreases with the decrease of PC MW. The extrapolated zero fracture energy was found at M_n = 6800 or MFR = 135. The G_c of the elastomer-modified PC (MFR = 15, 5% elastomer) is about twice that of thee unmodified one. The presence of elastomer in the PC matrix promotes the plane–strain localized shear yielding to greater extents and thus increases the impact strength and G_c in a typically brittle fracture. Two separate modes, localized and mass shear yielding, work simultaneously in the elastomer-toughening mechanism. The plane–strain localized shear yielding dominates the toughening mechanism at lower temperatures and brittle failure, while the plane–stress mass shear yielding dominates at higher temperatures and ductile failure. For the elastomer-modified PC (10% elastomer), the estimated extension ratio of the yielding zone of the fractured surface is 2 for the ductile failure and 5 for the brittle crack. A criterion for shifting from brittle to ductile failure based on precrack critical plastic-zone volume is proposed.     

Kinetics of fatigue and creep crack propagation in PVC pipe

The kinetics of creep and fatigue crack growth in PVC pipe were studied in order to develop a methodology for predicting long‐term creep fracture from short‐term fatigue tests. Fatigue and creep crack propagation followed the conventional Paris law formulations with the same power 2.7: da/dt = A_fΔK^2.7_I and da/dt = BK^2.7_I, respectively. The activation energy for creep crack propagation, obtained from the temperature dependence of the Paris law prefactor, allowed extrapolation of high temperature creep fracture to low temperature creep crack growth rates. The activation energy for fatigue crack propagation was much lower than that for creep. Therefore, fatigue and creep could not be directly correlated by using the prefactor in the covenentional Paris law formulations. Furthermore, a unique value of the Paris law prefactor did not describe frequency and R‐ratio (amplitude) effects in fatigue crack propagation. Nevertheless, conformity of crack growth rates measured under all conditions to the same Paris law power suggested that correlation should be sought in alternative formulations of the crack growth rate.     

Fracture characterization of recycled high density polyethylene/nanoclay composites using the essential work of fracture concept

The effect of nanoclay on the plane‐strain fracture behavior of pristine High density polyethylene (HDPE) and recycled HDPE blends was studied using the essential work of fracture (EWF) concept. The failure mode of EWF tested specimens was found to be associated with the specific non‐EWF (β_Bw_p,B). Adding 6‐wt% of nanoclay to pristine HDPE and 2‐wt% to recycle‐blends greatly decreased the β_Bw_p,B values and led to a transition from ductile to brittle failure mode. A fractographic study revealed that the difference in failure modes was caused by the changes in micro and macro morphologies, which could be related with the specific EWF (w_e,B). In the ductile failure, w_e,B is governed by the fibril size; adding nanoclay and recycled HDPE to pristine HDPE decreased the fibril size and subsequently lowered the w_e,B value. In the brittle failure, the w_e,B value was enhanced by creating a rough fracture surface. Adding nanoclay to pristine HDPE, a steadily decrease in w_e,B was measured until 4‐wt% after which the change was insignificant. Conversely, nanoclay content more than 2‐wt% in recycle‐blends greatly decreased the w_e,B value. A transition map was constructed to illustrate the potential failure mode and the associated fracture morphology based on the tested material compositions. POLYM. ENG. SCI., 56:222–232, 2016. © 2015 Society of Plastics Engineers     

A fatigue crack initiation map for polycarbonate

The mechanisms of fatigue crack initiation for various stress levels and thicknesses have been determined for single-edge notched specimens of polycarbonate and used to assemble a map. Three basic fatigue crack initiation mechanisms were identified and named as cooperative ductile (the damage zone formed ahead of crack consisting of yielded material), solo-crack brittle (very little damage zone development), and cooperative brittle (identified as a cloud of microcracks or crazes that developed at the notch tip). With a given applied stress and within the same failure mechanism, the values of the number of cycles to crack initiation decrease with increase in thickness. The transition from cooperative ductile to solo-crack brittle initiation mechanisms is sudden with increasing thickness. Transition from cooperative ductile to cooperative brittle with decreasing stress was less well defined. Regions where combinations of mechanisms were observed are also identified in the map. © 1993 John Wiley & Sons, Inc.     

Fatigue crack growth in polymers. II. The interaction of mean stress,frequency, and temperature

Fatigue crack propagation was studied in large centernotched plate specimens of two polymers, poly(methyl methacrylate) and polycarbonate, under tensile cycling conditions. Tests were performed at frequencies of 0.1, 5.0, and 20 Hz, and at two temperatures, ?60 and +21°C. The interaction of mean stress intensity, frequency and temperature was investigated. It was found that in tests performed at constant frequency or temperature, the fatigue crack propagation rates were dependent on both the range of the applied stress intensity factor and its mean value, K_m. All propagation rates increased with increasing K_m. Also, the threshold stress intensities decreased with increasing K_m, suggesting very low levels of ΔK for non-propagating cracks, certainly below the 0.4 K_c, the minimum level investigated here. In PMMA, decreasing crack growth rates with increasing frequency were established for a wide range of K_m. However, in PC crack growth rates increased substantially with increasing frequency. Finally, “upper and lower transition points” were noted on crack growth curves of both materials.     

Fatigue crack propagation behavior of polyether ether ketone under biaxial loading

Polyether ether ketone (PEEK) has become a promising material in total joint replacement. However, it still faces the risk of fatigue fracture during service. In this paper, the effects of biaxial stress ratio λ, cyclic stress ratio R, and load phase difference θ on fatigue crack propagation (FCG) behavior of PEEK are investigated. In the case of vertical cracks, results show that the FCG rate of PEEK increases with the R value, while decreases with the increase of λ value. Furthermore, the effective stress intensity factor range ΔK_eff can uniformly describe the biaxial FCG behavior at different cyclic stress ratios. In the case of 45° slant cracks, compared with mode-I intensity factor range ΔK_I, the energy release rate range ΔG is more accurate for describing the FCG behavior under various load phase differences. In addition, the investigation on the 45° crack propagation path shows that a bifurcated Y-shaped crack appears under 180° load phase difference, while no bifurcated crack appears under 90° load phase difference and uniaxial loading. Three different methods are used to predict the crack propagation path. The comparison results show that the maximum circumferential stress (MTS) criterion can well predict the crack propagation path under out-of-phase biaxial loading and uniaxial loading.     

Dynamic stress intensity factors during viscoelastic crack propagation at various strain rates

Dynamic stress intensity factors K_D were measured by the caustic method and crack propagation velocity ? by the velocity gauge techniques for PMMA [poly(methyl methacrylate)] during dynamic crack propagation at various strain rates \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} . No definite applied strain rate effects on the dynamic stress intensity factor were observed for applied strain rates ranging from 8.33 × 10^?4 to 30/sec; however, the test results do show crack propagation velocity dependency in K_D ～ ? relations. The high local strain rate region may be realized at the running crack tip even under the quasi-static loading case of \documentclass{article}\pagestyle{empty}\begin{document}$ \rm \dot \varepsilon $\end{document} = 8.33 × 10^?4/sec, since all the crack propagation velocities obtained were greater than 50 m/sec even up to 450 m/sec.     

Unstable fracture of rubber-toughened polymers

The goal of this investigation has been to obtain a useful criterion for the onset of ductile instability. Notched 3-point bend samples of 4 impact-modified plastics were tested under load-controlled conditions to enhance the instability. Neither plastic collapse of the remaining ligament nor large scale yielding at the crack tip was observed, although significant damage zone development and sub-critical crack growth were observed prior to crack instability. The stress intensity factor at instability (K_c) was found to be independent of crack length for the plastics tested. More surprisingly, when K_c was normalized by the corresponding yield stress, this normalized value was found to be experimentally the same for these four impact modified polymers. Calculations based on ductile tearing instability theory were ambiguous and inconclusive. These results suggest that linear fracture mechanics criteria in load controlled tests may still be applicable for engineering purposes under what has normally been considered ductile conditions.