EXPERIMENTAL STUDY OF CRACK-INDUCED DYNAMIC DAMAGE GROWTH IN FIBRE COMPOSITES

SUMMARY

The fracture process in composites proceeds by the formation and propagation of a damage zone. The microfracture mechanisms within the damage zone are primarily responsible for energy absorption and dissipation in the macroscopic fracture and, consequently, influence fracture toughness of composites. With this in mind, crack-induced dynamic damage growth has been studied in transparent glass-polyester composites with chopped strand mat and woven fabric as reinforcements. Damage growth has been recorded by photographing the specimens in quick succession using a Cranz-Schardin-type multiple spark camera.

The dynamic damage zone has been observed to propagate, similar to static growth, generally perpendicular to the loading direction; but sometimes the damage zone splits analogous to crack branching in homogenous materials. Higher fibre volume fraction reduces linear damage propagation and increases damage spread in other directions. Damage propagation velocity in the composite appears to be slightly lower than the crack propagation velocity in a polyester resin.     

起爆方式对岩石爆破裂纹扩展影响的实验分析

为了了解硬岩爆破施工中,提高炸药能量利用率的最佳起爆方式或药包结构,在聚能作用和岩石破碎理论的基础上,分析了空穴聚能、爆轰聚能的聚能作用和爆破裂纹产生机理及准则。通过实验研究了中心雷管、空穴聚能和爆轰聚能的装药方式下爆破裂纹扩展规律。结果表明,3种装药方式下的岩石破碎区范围相差不大,但是中心雷管起爆时岩石径向裂纹较均匀,空穴聚能时在聚能罩的方向上形成较宽、较长的爆破裂纹,爆轰聚能在起爆点中心轴线上形成大的扩展裂纹,虽其宽度和长度均略小于空穴聚能装药,但该方法避免了金属材料的消耗和繁琐的施工工艺。结合红沿河核电站取水隧洞盾构孤石预裂爆破施工,开展的爆轰聚能的工业应用实验表明,采用爆轰聚能爆破技术使孤石强度大幅降低,减少了孤石对盾构机刀盘的磨损,避免了卡钻现象,使盾构机掘进速率提升至10.42mm/min,极大的提高了施工效率。研究结果对起爆技术改进和夹制力大的孤石爆破具有一定的指导意义。     

单向静压下柱状炮孔端部爆生裂纹的扩展规律

高地应力对岩层地下工程爆破动态断裂过程有重要影响。采用数字激光动态焦散线测试系统,研究了不同单向静压下柱状炮孔端部爆生裂纹动态断裂行为,明确了柱状炮孔端部爆生裂纹的扩展规律。结果表明:单向静压越大,端部裂纹平均扩展长度越短,但单向静压下端部裂纹尖端积聚能量的快速释放会导致裂纹初始扩展速度提升;裂纹尖端应力强度因子基本随单向静压增加而递减,单向静压越大,应力强度因子随时间下降越剧烈,裂纹的止裂韧度越高,止裂时间越早;单向静压作用下的爆生裂纹在整个扩展阶段基本表现为I型裂纹,无静压作用下爆生裂纹在扩展初期表现为I型裂纹,中后期表现为复合型裂纹。研究结果对认识静压作用下的柱状炮孔端部破坏机理具有一定意义。     

Analytical modelling of dynamic fracture and crack arrest in DCB specimens under fixed displacement conditions

An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded double cantilever beam (DCB) specimen. Fixed displacement condition is prescribed at the pin location under which crack arrest occurs. In the static case, at first, the compliance function of a DCB specimen is obtained and shows good agreement with the experimental results cited in the literature. Afterward, the stress intensity factor is determined at the crack tip via the energy release rate formula. In the dynamic case, the obtained governing equations for the model are solved supposing quasi‐static treatment for unstable crack propagation. Finally, a closed form expression for the crack propagation velocity versus beam parameters and crack growth resistance of the material is found. It is shown that the reacceleration of crack growth appears as the crack tip approaches the finite boundary. Also, the predicted maximum crack propagation velocity is significantly lower than that obtained via the Euler–Bernoulli theory found in the literature.     

Dynamic crack propagation in rubber-modified composite models

The dynamic crack propagation behaviour of several rubber-modified composite models has been studied. In all cases the method of high speed photography along with the method of dynamic caustics was used. Results of crack propagation mode observation, fracture toughness and crack propagation velocity measurements are presented here. Especially in the case of two complex inclusions it was found that the crack propagation mode is highly rate dependent. At low test rates the crack growth tends to follow an almost straight crack path while an increase in strain rate in general results in the formation of a kink in the interparticle area. In the same area a crack propagation delay, and in some cases arrest, was observed while both the crack propagation velocity v and dynamic stress intensity factor K _i ^d showed an intense variation. For the sake of comparison, specimens with one and/or two press-fitting inclusions as well as with two holes were fractured under dynamic loads. In all cases both qualitative and quantitative results were obtained.     

Crack propagation velocities in bi-phase plates under static and dynamic loading

An investigation of the dependence of the crack-propagation velocity in complex bimaterial plates at different loading rates was undertaken. The specimens were fractured under the influence of both static and dynamic loadings and the crack-propagation velocities were detected by high speed photography with the optical method of caustics.The investigation was concentrated in detecting the influence that the different loading rates have on the fracture velocities in both phases of the plates and how this influence interferes—counteracting or superimposing—with the other factors that determine the crack propagation process in bi-material specimens. These factors are the effect of interface, the influence of the mechanical characteristics of each phase on the crack-propagation velocity etc.The results show that for constant and given material characteristics of the bi-phase plate the crack propagation velocity in the first (notched) phase tends to increase with increasing strain rates.The same is valid for the crack propagation velocity in the second phase, but only for the case when fracture occurs under the influence of a dynamic load. A significant discrepancy of the latter statement occurs, however, in the case of fracture under a continuously-increasing static load. In this case the crack-propagation velocity in the second phase reaches some remarkably high values, which are of the order of high strain-rate dynamic crack propagation velocities.In this way, the crack-arrest effect on the crack propagation velocity appears to be more significant in the case of a static loading than it is for the case of dynamic loading.     

A non-equilibrium thermodynamic model for the crack propagation rate

A non-equilibrium thermodynamics-based evolution model describes the nonsteady, crack propagation rate for both brittle fracture and for viscoplastic behavior at the crack tip. This model for dynamic crack propagation under dynamic or quasi-static loading is developed from an energy functions viewpoint and extends a non-equilibrium thermodynamics construction based on a instantaneous maximum dissipation criterion and a thermodynamic relaxation modulus that permits multi-scale modeling. The evolution equations describing the non-equilibrium fracture process are generated from a generalized energy function whose zero gradient manifold gives the assumed quasi-static crack propagation equations. The class of models produced includes the classical Freund model and a modification that is consistent with the experimental maximum crack velocity. In unstable propagation, the non-equilibrium process is repelled from the quasi-static manifold. If the initial state is stable, then the crack growth process approaches the quasi-static manifold and eventually the crack is arrested. An application of the construction gives the craze growth in PMMA. A simple viscoplastic model for metals predicts the change in temperature at the crack tip as the crack grows.     

Stable crack growth,instability, fatigue and fracture of a 50/50 blend of poly(2,6-dimethyl-1,4-phenylene oxide) and polystyrene

The fracture behaviour of a 50/50 blend of poly(2,6-dimethyl-1,4-phenylene oxide)/poly-styrene has been studied. The crack propagation behaviour is strongly influenced by the temperature, crack driving force and the nature of the crack tip craze zone. A fracture map outlining the regions of stable crack growth as a function of temperature, crack velocity and crack driving force has been determined. At high temperatures and low crack growth velocities, stable crack propagation proceeds through a single-craze crack tip damage zone, while at lower temperatures and high crack velocities, a multiple-craze crack tip zone is observed. Corresponding behaviour can be observed under fatigue loading conditions. An instability leading to very high-speed fracture occurs at a critical crack velocity, thus limiting the stable crack propagation regime to lower velocities. The various reported measures of fracture toughness, such as those based on crack initiation, peak load and the onset of crack instability, are discussed.     

Correlation of stepwise fatigue and creep slow crack growth in high density polyethylene

The kinetics and mechanism of slow crack growth in fatigue and creep of high density polyethylene were studied. The relationship between fatigue and creep was examined by varying the R-ratio (the minimum/maximum loads in the fatigue loading cycle) in the tensile mode such that loading ranged from mainly dynamic (R = 0.1) to static (R = 1.0, creep test). The stepwise crack propagation mechanism characteristic of long-term failures in polyethylene was observed for all loading conditions studied. Fatigue fracture kinetics allowed for extrapolation to the case of creep failure, which suggested that short-term fatigue testing can be used to predict long-term creep fracture properties. The size of the craze damage zone ahead of the arrested crack tip was controlled only by the mean stress, however the lifetime of the zone was determined by both the maximum stress and the mean stress. Crack growth rate was related to the maximum stress and the mean stress by a power law relationship, which described crack growth over the entire range of loading conditions studied.     

Double torsion testing of high velocity crack resistance

Field tests show that cracks can propagate steadily at more than 300 m sec^–1 along gas-pressurized pipelines of normally ductile polyethylene, once initiated by impact. Although the determination of safe operating conditions demands a knowledge of the pipe material's resistanceR to such high-velocity cracks, devising an appropriate small-scale test presents major problems. Instrumented drop-weight testing of double torsion specimens offers a promising solution: constant-velocity brittle crack propagation is observed and, since the static deformation mode remains admissible in the dynamic régime, a simple analysis is possible. From displacement data, this provided quite consistent results up to 200 m sec^–1 crack velocity, whilst load measurements were more affected by transient torsional wave propagation. A simple dynamic analysis satisfying more boundary conditions supports the displacement-based quasi-static results, and offers to extend the method to higher crack velocities.     

The initiation of slow crack growth in linear polyethylene under single edge notch tension and plane strain

The kinetics and microstructural changes associated with the initiation of slow crack growth in PE were measured. The initiation process consists of an instantaneous deformation zone which grows at a constant velocity until the beginning of fracture. The velocity of the damaged zone accelerates when the fibril fracture begins at the root of the initial notch. It was found that the initial velocity of the deformation zone depended on stress to about the 4th power and had an activation energy of about 100 kJ mol^–1; these results are about the same as those found by Chan and Williams for the crack growth velocity. It is concluded that both crack initiation and crack growth are governed by the same fundamental process, notably fibril thinning.     

A finite element investigation of quasi-static and dynamic asymptotic crack-tip fields in hardening elastic-plastic solids under plane stress

The asymptotic structures of crack-tip stress and deformation fields are investigated numerically for quasi-static and dynamic crack growth in isotropic linear hardening elastic-plastic solids under mode I, plane stress, and small-scale yielding conditions. An Eulerian type finite element scheme is employed. The materials are assumed to obey the von Mises yield criterion and the associated flow rule. The ratio of the crack-tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 × 10⁴. The results of this study strongly suggest the existence of crack-tip stress and strain singularities of the type r ^s (s < 0) at r=0, where r is the distance to the crack tip, which confirms the asymptotic solutions of variable-separable type by Amazigo and Hutchinson [1] and Ponte Castañeda [2] for quasi-static crack growth, and by Achenbach, Kanninen and Popelar [3] for dynamic crack propagation. Both the values of the parameter s and the angular stress and velocity field variations from the present full-field finite element analysis agree very well with those from the analytical solutions. It is found that the dominance zone of the r ^s-singularity is quite large compared to the size of the crack-tip active plastic zone. The effects of hardening and inertia on the crack-tip fields as well as on the shape and size of the crack-tip active plastic zone are also studied in detail. It is discovered that as the level of hardening decreases and the crack propagation speed increases, a secondary yield zone emerges along the crack flank, and kinks in stress and velocity angular variations begin to develop. This dynamic phenomenon observable only for rapid crack growth and for low hardening materials may explain the numerical difficulties, in obtaining solutions for such cases, encountered by Achenbach et al. who, in their asymptotic analysis, neglected the existence of reverse yielding zones along the crack surfaces.     

静态破碎剂膨胀作用下试件裂纹扩展试验研究

采用高速摄像技术,进行了静态破碎剂作用下材料破坏的物理试验,研究了膨胀作用下含切槽孔模型材料的动态断裂力学行为,获得了裂纹扩展速度和裂纹扩展加速度的变化规律。研究结果表明:静态破碎剂作用下含两翼切槽孔试件产生两条基本成直线的裂纹,裂纹扩展速度和加速度的变化基本是呈现先增加后降低的趋势;裂纹扩展加速度最大值到达的时间早于裂纹扩展速度到达最大值的时间;裂纹的萌生、扩展到最后的失稳过程非常明显。研究结果可为静态破碎剂在实际工程中的应用提供理论指导。     

Analysis of the fracture behaviour of a stitched single-lap joint

The effect of stitching on the fracture response of single-lap composite joints was studied by a combined experimental and numerical analysis. Unstitched and Kevlar stitched joints were tested under static and fatigue loading to characterize damage progression and failure modes; a three-dimensional finite element analysis was carried out to evaluate the influence of stitches on strain energy release rates as a function of damage and to identify the role of various stitching parameters on the fracture behaviour of joints.It was observed that the failure of the joints occurs as a consequence of the propagation of delamination at the interface between the adherends; the propagation is stable under fatigue loads and unstable under static loads. Stitching does not improve the static strength of joints but significantly prolongs the duration of the crack propagation phase under fatigue loading.The results of finite element modelling indicate that the incorporation of stitches reduce G_I to zero after the delamination front passes the stitch line, but it is not effective in reducing mode II energy release rate. They also show that strain energy release rates are not greatly affected by the length of stitch-laminate debonding, which, conversely, does influence stitch tensioning. Moreover, 3D analysis reveals that stitches become less efficient in reducing the crack driving force with increasing stitching steps.     

Effect of microstructural modification on damage tolerance of 34CrMo4 shaft steel

Overall damage tolerances of the heat‐treated 34CrMo4 steels having ferritic‐pearlitic, bainitic, and tempered‐martensitic microstructures were evaluated based on their threshold stress intensity factor prior to small crack propagation, fatigue strength, and fracture toughness under static loading. Kitagawa‐Takahashi diagrams were constructed to determine the limiting size of small crack propagation. The micromechanical effects of carbide morphology and phase distribution on quasi‐static and dynamic mechanical properties were also elaborated. Fractographic investigations were carried out on the notched fatigue test specimens to distinguish deterioration and deformation mechanism of the microstructure under reversed cyclic loads. Finally, improvements in the damage tolerance were discussed to present the advantages and disadvantages of each heat treatment procedure to minimize in‐service fatigue failures.     

Inertial effects on fatigue crack growth

In this paper, a cohesive zone model is used to study the influence of inertial effects on crack growth considering cyclic loading in homogenous rate‐independent materials. Quasi‐static and dynamic solutions are compared in order to establish the conditions in which the inertial effects become important in the analysis. It is discussed how speed and frequency of the loading and specimen sizes modify crack growth characteristics. In general, an increase in the loading frequency leads to a higher propagation velocity. Very high loading frequencies may lead to the formation of microcracks ahead of the crack tip and may change the failure mode of the cracked structure from crack propagation to uniform debonding. This work shows that inertial effects are specially noticeable for frequencies in the kHz range. However, applied frequencies close to natural frequencies of the cracked specimen can give rise to strong inertial effects and then a substantial reduction of fatigue life for much lower frequencies. This work also shows that critical frequencies depend on the specimen size.     

Slow fracture in a homopolymer and copolymer of polyethylene

The slow crack-growth behaviours of a high-density polyethylene and an ethylene-hexene copolymer with 4.5 butyl chains per 1000 carbon atoms are compared. The slow crack-growth rate in the copolymer is about 10² to 10³ times slower than for the homopolymer. The two polymers are compared with respect to their kinetics of slow crack growth, the morphology of the damage zone that grows from a notch, the stress-strain behaviour and the temperature dependence of the rate of damage. The results suggest that the major effect of the butyl branches is to decrease the rate of disentanglement which governs the process of slow crack growth.     

CORROSION FATIGUE OF MILD STEELS IN A SODIUM NITRATE SOLUTION

Abstract— Cyclic loading of mild steels in 4 N NaNO₃ produces intergranular cracking similar to that associated with stress corrosion cracking at static loads, even when the cyclic loads are below the threshold for cracking under static conditions. However, under some circumstances cyclic loading promotes transgranular crack growth, the velocity of which may increase or decrease with increasing stress intensity factor. The transition from intergranular to transgranular cracking, or vice versa, is determined by the relative velocities of the two modes of failure, that observed having the higher velocity. The suppression of transgranular cracking as the stress intensity factor increases is only observed when the loading involves a compressive component and the effect is explained in terms of corrosion products interfering with the cracking process. Tension-tension loading in nitrates produces crack growth characteristics similar to those observed in oil.     

Fatigue propagation of short and long cracks in gaseous hydrogen environment in 3.5NiCrMoV steel

Turbo generators for nuclear plants are mostly equipped with hydrogen cooling systems. Current practice of characterizing the growth of fatigue cracks on the basis of fracture mechanics primarily relies on fatigue tests for long cracks which are typically of several millimeters in length. However, in view of extended life for the plants, the damage tolerance evaluation of such fatigue-critical engineering components requires understanding of the propagation of cracks of significantly smaller dimensions. Then the near threshold of short cracks is investigated and compared to the behavior of long crack by experiments under 4 bar hydrogen atmosphere. The short crack fatigue propagation in hydrogen atmosphere is shown similar to that in air, growing faster than the long crack and at ΔK ranging below the long crack threshold; this effect is related to a reduced crack closure shielding. The propagation behavior of long crack under hydrogen atmosphere is shown similar to that obtained in air in the low rate range, i.e. when the maximum of the stress intensity factor K_max is lower than a critical level of about 16 MPa m^1/2 with higher crack growth rate than in high vacuum. This environment effect is related to the presence of residual water vapor in both gases. For higher K_max, much faster growth rates under hydrogen atmosphere in comparison to air and vacuum are observed and related to hydrogen assisted intergranular propagation combining fatigue and sustained loading damage. The results are discussed on the basis of micrographic observations supporting the involved mechanisms.     

Rißfortschritt in ultrafesten Stählen und deren Schweißverbindungen bei dynamischer Beanspruchung

Crack propagation in ultra-high-strength steels and their welded joints under dynamic loading . Reported are results of investigation into the propagation of cracks in the base metal and weld metal of an ultra-high-strength steel. The material used in the investigations was a Ni? Co? Mo? alloy maraging steel with a yield point of 170 kp/mm². The steel was arc welded and TIG welded. The joints exhibited a drop of static strength in the range of 5 to 8 percent related to the base metal. Under zero-to-tension stress cycles the fatigue strength corresponded that of other high-strength steels, under tension-compression stress cycles the steel exhibited a higher fatigue strength. It was possible to show striations with the aid of scanning microscopy. Comparing the track propagation calculated in the microscopic range with the results obtained from the crack growth curves produced approximate agreement.