The mechanics of matrix cracking in brittle-matrix fiber composites

Matrix fracture in brittle-matrix fiber composites is analyzed for composites that exhibit multiple matrix cracking prior to fiber failure and have purely frictional bonding between the fibers and matrix. The stress for matrix cracking is evaluated using a stress intensity approach, in which the influence of the fibers that bridge the matrix crack is represented by closure tractions at the crack surfaces. Long and short cracks are distinguished. Long cracks approach a steady-state configuration, for which the stress intensity analysis and a previous energy balance analysis are shown to predict identical dependence of matrix cracking stress on material properties. A numerical solution and an approximate analytical solution are obtained for smaller cracks and used to estimate the range of crack sizes over which the steady-state solution applies.     

Micromechanical modeling of unidirectional continuous sigma fiber-reinforced Ti-6Al-4V subjected to transverse tensile loading

A micromodeling analysis of unidirectionally reinforced Ti-6-4/SM1140+ composites subjected to transverse tensile loading has been performed using the finite-element method (FEM). The composite is assumed to the infinite and regular, with either hexagonal or rectangular arrays of fibers in an elastic-plastic matrix. Unit cells of these arrays are applied in this modeling analysis. Factors affecting transverse properties of the composites, such as thermal residual stresses caused by cooling from the composite processing temperature, fiber-matrix interface conditions, fiber volume fraction, fiber spacing, fiber packing, and test temperature are discussed. Predictions of stress-strain curves are compared with experimental results. A hexagonal fiber-packing model with a weak fiber-matrix interfacial strength predicts the transverse tensile behavior of the composite Ti-6-4/SM1140+ most accurately.     

Effects of interfacial strength on fatigue crack growth in a fiberreinforced Ti-alloy composite

The fatigue crack growth behavior of a Ti-6A1-4V composite with boron fibers was previously studied in the as-received and thermally exposed conditions. Fracture strengths of the composite, fiber, and interface were characterized together with fatigue crack growth rates and failure mechanisms. Utilizing the matrix and fiber properties as input, a recently proposed model was exercised to elucidate the effects of interfacial strength on crack growth rates in the composite. Comparison of experimental results with model calculations revealed that a weak fiber/matrix interface combined with a strong, high-modulus fiber led to interface debonding and crack deflection and produced the beneficial effects of increased threshold and reduced transverse crack growth rates. This paper is based on a presentation made in the symposium “Interfaces and Surfaces of Titanium Materials” presented at the 1988 TMS/AIME fall meeting in Chicago, IL, September 25–29, 1988, under the auspices of the TMS Titanium Committee.     

Nonlinear Fracture Analysis of Delamination Crack Jumps in Laminated Composites

As part of the quest to add the infraply scale to high-fidelity simulations of damage evolution in composites, a model of the phenomenon of delamination jumping across transverse plies is formulated by using nonlinear cohesive fracture models in the augmented finite element method (A-FEM). The nonlinearity of the fracture process zone and the interaction between multiple cracks combines to determine the details of how the delamination jump occurs. Simulations reveal that the jumping process starts with the triggering of a sequence of kinking cracks branching from the propagating delamination crack into the transverse plies. The first few kinking cracks arrest within the transverse plies just above the further interface because of the crack-retarding effects of the nonlinear process zone and the effects of material heterogeneity. Eventually, one kinking crack reaches the interface and initiates a new delamination crack, a step that is accompanied by a significant load spike. The competition between delamination and kinking cracks shows global-local coupling: kinking cracks are triggered when the local stress satisfies a critical condition, but a kinking crack does not reach the second interface and initiate the new delamination crack until the global energy release rate reaches the kinking crack toughness. This suggests that the jumping process is controlled more by deterministic load and geometrical factors than by stochastic flaw populations.     

Failure mechanisms in SiC-fiber reinforced 6061 aluminum alloy composites under monotonic and cyclic loading

Micromechanisms influencing crack propagation in a unidirectional SiC-fiber (SCS-8) continuously reinforced Al-Mg-Si 6061 alloy metal-matrix composite (SiC_f/Al-6061) during monotonie and cyclic loading are examined at room temperature, both for the longitudinal (0 deg or L-T) and transverse (90 deg or T-L) orientations. It is found that the composite is insensitive to the presence of notches in the L-T orientation under pure tension loading due to the weak fiber/matrix interface; notched failure strengths are ∼1500 MPa compared to 124 MPa for unreinforced 6061. However, behavior is strongly dependent on loading configuration, specimen geometry, and orientation. Specifically, properties in SiC_f/Al in the T-L orientation are inferior to unreinforced 6061, although the composite does exhibit increasing crack-growth resistance with crack extension (resistance-curve behavior) under monotonie loading; peak toughnesses of ∼16 MPa√m are achieved due to crack bridging by the continuous metal phase between fibers and residual plastic deformation in the crack wake. In contrast, such bridging is minimal under cyclic loading, as the ductile phase fails subcritically by fatigue such that the transverse fatigue crack-growth resistance is superior in the unreinforced alloy, particularly at high stress-intensity levels. Conversely, fatigue cracks are bridged by unbroken SiC fibers in the L-T orientation and exhibit marked crack deflection and branching; the fatigue crack-growth resistance in this orientation is clearly superior in the composite.     

Crack Growth Resistance of Hybrid Fiber-Reinforced Cement Matrix Composites

The effect of hybrid fiber reinforcement on fracture energy and crack propagation in cement matrix composites is examined. The crack in cement matrix composites is allowed to fracture under mode-I loading with three-point bending beam specimens. The influence of fiber types and their combination is quantified by using the toughness index and fracture energy. A proper hybrid combination of steel fibers and polyvinyl alcohol microfibers enhances the resistance to both the nucleation and growth of the crack. The micromechanical model of hybrid composites by using a fiber bridging law is emphasized, and the numerical model prediction closely matches the behavior obtained from the experiment. The influencing role of the material parameters in the fracture tests (e.g., the fracture toughness index and fracture energy) becomes more apparent than ones used in some conventional strength-based or fiber pullout tests, and these fracture parameters could screen the effect of fiber/microfiber reinforcement in enhancing the crack growth resistance of cementitious composites. This study demonstrates that fundamental fracture tests are effective to characterize and develop high-performance hybrid fiber–reinforced cement matrix composites.     

C/C复合材料SiC涂层裂纹形貌及分布的研究

由于涂层与C/C复合材料之间热膨胀系数不匹配,当冷却至室温时在高温下制备的抗氧化涂层会产生裂纹,为分析涂层裂纹的组态,通过在碳毡和真空穿刺两种C/C复合材料基体上制备单层、双层SiC涂层来研究涂层裂纹的形貌及分布.利用金相显微镜和扫描电镜观察两种涂层裂纹的形貌和分布,解释了裂纹与涂层所受热应力及基体原有缺陷的关系,利用XRD分析了单层和双层涂层的成分,说明了不同类型SiC结构与涂层裂纹之间的联系.结果表明涂层裂纹分布及裂纹宽度与基体纤维方向有关;随着涂层厚度增大,微裂纹数量减少;基体原有缺陷会导致涂层产生穿透性裂纹.     

On creep of unidirectional fiber composites with fiber damage

The roles of broken fibers in the creep of continuous fiber reinforced composites are studied theoretically. The unidirectional fiber composite is modeled using a cylindrical cell consisting of a single broken fiber and a shell of the fiber material embedded in an elastic-power law creeping matrix. The time-dependent creep behavior of the composite is calculated using finite elements; both longitudinal and transverse loads are considered. It is shown that when fibers are broken, the increase in the overall creep strain of the composite and the axial stress in the intact fibers can be significant. It is also demonstrated that applied transverse tension can reduce the composite creep strain and the normal stress in the fibers; the opposite is true with applied transverse compression. Matrix plasticity is found to have very limited effect on the creep behavior of the composite. The accuracy of the McLean formula for undamaged composite is also examined.     

The transverse creep deformation and failure characteristics of SCS-6/Ti-6AI-4V metal matrix composites at 482 °C

While continuous fiber, unidirectional composites are primarily evaluated for their longitudinal properties, the behavior transverse to the fibers often limits their application. In this study, the tensile and creep behaviors of SCS-6/Ti-6Al-4V composites in the transverse direction at 482 °C were evaluated. Creep tests were performed in air and argon environments over the stress range of 103 to 276 MPa. The composite was less creep resistant than the matrix when tested at stress values larger than 150 MPa. Below 150 MPa, the composite was more creep resistant than the unreinforced matrix. Failure of the composite occurred by the ductile propagation of cracks emanating from separated fiber interfaces. The environment in which the test was performed affected the creep behavior. At 103 MPa, the creep rate in argon was 4 times slower than the creep rate in air. The SCS-6 silicon-carbide fiber’s graphite coating oxidized in the air environment and encouraged the separation of the fiber-matrix interface. However, at higher stress levels, the difference in behavior between air- and argon-tested specimens was small. At these stresses, separation of the interface occurred during the initial loading of the composite and the subsequent degradation of the interface did not affect the creep behavior. Finally, the enrichment of the composite’s surface by molybdenum during fabrication resulted in an alloyed surface layer that failed in a brittle fashion during specimen elongation. Although this embrittled layer did not appear to degrade the properties of the composite, the existence of a similar layer on a composite with a more brittle matrix might be very detrimental.     

Prediction of creep-rupture life of unidirectional titanium matrix composites subjected to transverse loading

Titanium matrix composites (TMCs) incorporating unidirectional fiber reinforcement are considered as enabling materials technology for advanced engines which require high specific strength and elevated temperature capability. The resistance of unidirectional TMCs to deformation under longitudinally applied sustained loading at elevated temperatures has been well documented. Many investigators have shown that the primary weakness of the unidirectional TMC is its susceptibility to failure under very low transverse loads, especially under sustained loading. Hence, a reliable model is required to predict the creep-rupture life of TMCs subjected to different transverse stress levels over a wide range of temperatures. In this article, we propose a model to predict the creep-rupture life of unidirectional TMC subjected to transverse loading based on the creep-rupture life of unidirectional TMC subjected to transverse loading based on the creep-rupture behavior of the corresponding fiberless matrix. The model assumes that during transverse loading, the effective load-carrying matrix ligament along a row of fibers controls the creep-rupture strength and the fibers do not contribute to the creep resistance of the composite. The proposed model was verified using data obtained from different TMC fabricated using three matrix compositions, which exhibited distinctly different types of creep behavior. The results show that the creep-rupture life of the transverse TMC decreases linearly with increasing ratio of the fiber diameter to the ply thickness. The creeprupture life is also predicted to be independent of fiber spacing along the length of the specimen.     

Tensile properties of short fiber-reinforced SiC/Al composites: Part II. Finite-element analysis

The tensile properties of aluminum matrix composites containing SiC whiskers or particulate were investigated analytically and compared to experimental results. Two finite-element models were constructed and used for elastoplastic analysis. In both models, the SiC fibers are represented as longitudinally aligned cylinders in a three-dimensional array. The cylinder ends are transversely aligned in one model and staggered in the other. Using the models, the sensitivity of the predicted composite properties to the deformation characteristics of the matrix alloy was examined, and the general behavior of the models was validated. It was determined that both models are necessary to predict the overall composite stress-strain response accurately. The analytic results accurately predict: the observed composite stress-strain behavior; the experimentally observed increase in Young’s modulus and the work-hardening rate with increasing fiber volume content and aspect ratio; and the decrease and subsequent increase in proportional limit as the SiC volume fraction is increased. The models also predict that the transverse material properties should be insensitive to fiber aspect ratio. In addition, the model predicts the location of initial yielding and the propagation of the plastic region. These results offer insights into the deformation mechanisms of short fiber-reinforced composites.     

Crack propagation directions in unfilled resins

Posterior composite restorative materials undergo accelerated wear in the occlusal contact area, primarily through a fatigue mechanism. To facilitate the timely development of new and improved materials, a predictive wear model is desirable. The objective of this study was to develop a finite element model enabling investigators to predict crack propagation directions in resins used as the matrix material in composites, and to verify these predictions by observing cracks formed during the pin-on-disc wear of a 60:40 BISGMA:TEGDMA resin and an EBPADMA resin. Laser confocal scanning microscopy was used to measure crack locations. Finite element studies were done by means of ABAQUS software, modeling a cylinder sliding on a material with pre-existing surface-breaking cracks. Variables included modulus, cylinder/material friction coefficient, crack face friction, and yield behavior. Experimental results were surprising, since most crack directions were opposite previously published observations. The majority of surface cracks, though initially orthogonal to the surface, changed direction to run 20 to 30 degrees from the horizontal in the direction of indenter movement. Finite element modeling established the importance of subsurface shear stresses, since calculations provided evidence that cracks propagate in the direction of maximum K(II)(theta), in the same direction as the motion of the indenter, and at an angle of approximately 20 degrees. These findings provide the foundation for a predictive model of sliding wear in unfilled glassy resins.     

Ballistic Impact of Braided Composites with a Soft Projectile

Impact tests using a soft gelatin projectile were performed to identify failure modes that occur at high strain energy density during impact loading. Failure modes were identified for aluminum plates and for composites plates and half-rings made from triaxial carbon fiber braid having a 0/±60° architecture. For aluminum plates, a large hole formed as a result of crack propagation from the initiation site at the center of the plate. For composite plates, fiber tensile failure occurred in the back ply at the center of the plate. Cracks then propagated from this site along the ±60° fiber directions until triangular flaps opened to form a hole. For composite half-rings fabricated with 0° fibers aligned circumferentially, fiber tensile failure also occurred in the back ply. Cracks first propagated from this site perpendicular the 0° fibers. The cracks then turned to follow the ±60° fibers and 0° fibers until rectangular flaps opened to form a hole. Damage in the composites was localized near the impact site, while cracks in the aluminum extended to the boundaries.     

Matrix crack spacing in brittle matrix composites

A model describing the evolution of matrix cracks in undirectional continuous fiber, brittle matrix composites is developed. The approach involves calculation off the steady state strain energy release rate available for crack extension in terms of the constituent properties, the applied stress and the distances to the neighboring cracks. Interactions between cracks are found to occur when the crack spacing falls below twice the slip length. The model provides an analytical solution to the crack spacing for periodic arrays of cracks. Comparisons are conducted with predictions derived from computer simulations of random cracking. The effects of the matrix flaw density are briefly considered.     

Effect of fiber spatial arrangement on the transverse strength of titanium matrix composites

The transverse strength of titanium matrix composites (Ti-6Al-4V-SiC) with rectangular and hexagonal fiber arrangements was measured as a function of fiber volume fraction and cladding thickness. A net-section model was also developed to predict the strength as a function of fiber spatial arrangement. The model predictions are in good agreement with experimental results and recent finite element modeling (FEM) simulations. The data and model show that the transverse strength, for a fixed net fiber volume fraction, is strongly dependent on the cladding thickness, testing direction, and fiber spatial arrangement. The implications are particularly important for the design of rotating components such as rings or disks. For example, the transverse strength in the radial and axial directions can be tailored by using a rectangular fiber array and varying the cell aspect ratio. Another simple strategy for increasing the transverse strength, for an equivalent net fiber volume fraction, is to increase the cladding thickness. For some fiber arrangements, a locally high volume fraction composite surrounded by a thick cladding can be significantly stronger than a composite with a uniform fiber distribution.     

Fatigue crack growth in Ti-matrix composites with spatially varied interfaces

Spatially varied interfaces (SVIs) is a design concept for composite materials where the interface mechanical properties are varied along the length and circumference of the fiber/matrix interface. These engineered interfaces can be used to modify critical titanium matrix composite properties such as transverse tensile strength and fatigue crack growth resistance in ways that produce a balanced set of properties. The SVI approach may also be used to probe interface failure mechanisms for the purpose of understanding complex mechanical phenomena. Single lamina Ti-6Al-4V matrix composites containing strongly bonded SiC fibers were fabricated both in the as-received condition and with a weak longitudinal stripe along the sides of the fibers. The striped SVI composites exhibited an increase in the overall fatigue crack growth life of the specimens compared to the unmodified specimens. This improvement was caused by an increased extent of debonding and crack bridging in SVI composites. This article is based on a presentation made in the symposium “Fatigue and Creep of Composite Materials” presented at the TMS Fall Meeting in Indianapolis, Indiana, September 14–18, 1997, under the auspices of the TMS/ASM Composite Materials Committee.     

Transverse creep and stress-rupture of borsic-aluminum composites and borsic-aluminum composites containing stainless steel and titanium

The transverse creep and stress rupture behavior of a number of Borsic®-aluminum composites was investigated at temperatures from 200° to 400°C. The cpmposites studied consisted of nominally 50 vol pct Borsic fiber and included matrices of 6061, 2024, 2219, and 5052 aluminum alloys. The effect of heat treatment was studied in the heat-treatable alloys. Where transverse composite behavior differed from matrix alloy behavior, the difference was found to be due primarily to a change in fracture mode at higher matrix strength levels from matrix failure to one which involves longitudinal fiber splitting. Of the four basic matrix alloys tested, the best creep resistance was obtained with the 2024 matrix. Additional improvement of transverse creep and stress rupture resistance was realized by incorporating transverse reinforcements such as SAP alloy foil, titanium alloy foil, and 0.002 in. stainless steel wire in the composites. These reinforcements made possible good transverse properties at 400°C with density increases of ≤15 pct. The two best additions were 21 pctβ III titanium foil and 6 pct AFC-77 stainless steel wire. A transverse fracture mode incorporating longitudinal fiber splitting was documented and characterized, and its effect on composite behavior determined. The use of nonsplitting fibers such as 5.6 mil B and 5.7 mil Borsic in preventing this fracture mode was investigated.     

Ballistic Impact Properties of Zr-Based Amorphous Alloy Composites Reinforced with Woven Continuous Fibers

This study aims at investigating ballistic impact properties of Zr-based amorphous alloy (LM1 alloy) matrix composites reinforced with woven stainless steel or glass continuous fibers. The fiber-reinforced composites with excellent fiber/matrix interfaces were fabricated without pores and misinfiltration by liquid pressing process, and contained 35 to 41 vol pct of woven continuous fibers homogeneously distributed in the amorphous matrix. The woven-STS-continuous-fiber-reinforced composite consisted of the LM1 alloy layer of 1.0 mm in thickness in the upper region and the fiber-reinforced composite layer in the lower region. The hard LM1 alloy layer absorbed the ballistic impact energy by forming many cracks, and the fiber-reinforced composite layer interrupted the crack propagation and blocked the impact and traveling of the projectile, thereby resulting in the improvement of ballistic performance by about 20 pct over the LM1 alloy. According to the ballistic impact test data of the woven-glass-continuous-fiber-reinforced composite, glass fibers were preferentially fragmented to form a number of cracks, and the amorphous matrix accelerated the fragmentation of glass fibers and the initiation of cracks. Because of the absorption process of ballistic impact energy by forming very large amounts of cracks, fragments, and debris, the glass-fiber-reinforced composite showed better ballistic performance than the LM1 alloy.     

Micromechanics and fatigue crack growth in an alumina-fiber-reinforced magnesium alloy composite

A study has been made of fatigue crack growth through the magnesium alloy ZE41A and a composite of this alloy reinforced with alumina fibers. Crack growth rates were measured and failure mechanisms characterized for specimens with fibers parallel to the loading axis and for two off-axis orientations. Crack opening displacements and matrix and fiber strains in the vicinity of the crack tip were measured using the stereomaging technique. Crack growth rates through the composite were retarded by the fibers. For the composite with fibers at 22.5 deg to the loading axis, fibers were found to fracture in the composite at the same stress as measured for the fibers alone. Fiber fracture was the dominant growth-controlling mechanism for fibers oriented on and 22.5 deg to the loading axis, and little fiber pullout was observed. However, for crack growth through material with fibers oriented at 45 deg to the loading axis, crack growth was found to exist principally through the interface. Driving forces for cracks in interfaces were determined to be smaller than the applied δK. It was found that approximate fatigue crack growth rates through the composites could be predicted from those through the matrix by adjusting the tensile modulus. The upper and lower bounds of fatigue crack growth rate were also computed for the composite using a micromechanics-based model that incorporated observed failure mechanisms. A. McMINN, formerly with Southwest Research Institute, is with Failure Analysis Associates, Washington, D.C.     

Matrix cracking of cross-ply ceramic composites

A micromechanics study is presented of the matrix cracking behavior of laminated, fiber-reinforced ceramic cross-ply composites when subject to tensile stressing parallel to fibers in the 0° plies. Cracks extending across the 90° plies are assumed to exist, having developed at relatively low tensile stresses by the tunnel cracking mechanism. The problem addressed in this study is the subsequent extension of these initial cracks into and across the 0° plies. Of special interest is the relation between the stress level at which matrix cracks are able to extend all the way through the 0° plies and the well known matrix cracking stress for steady-state crack extension through a uni-directional fiber-reinforced composite. Depending on the initial crack distribution in the 90° plies, this stress level can be as large as the uni-directional matrix cracking stress or it can be as low as about one half that value. The cracking process involves a competition between crack bridging by the fibers in the 0° plies and interaction among multiple cracks. Crack bridging is modeled by a line-spring formulation where the nonlinear springs characterize the sliding resistance between fibers and matrix. Crack interaction is modeled by two representative doubly periodic crack patterns, one with collinear arrays and the other with staggered arrays. Material heterogeneity and anisotropy are addressed, and it is shown that a homogeneous, isotropic average approximation can be employed. In addition to conditions for matrix cracking, the study provides results which enable the tensile stress-strain behavior of the cross-ply to be predicted, and it provides estimates of the maximum stress concentration in the bridging fibers. Residual stress effects are included.