Deformation and fracture of a particle-reinforced aluminum alloy composite: Part II. Modeling

In this article, the tensile and fracture properties of a discontinuously reinforced aluminum (DRA) alloy composite are modeled to determine the influence of constituent parameters on material behavior. Comparison of the elastic-modulus calculations to the experimental data suggest that the angular particles are more effective in load transfer than spherical particles, and that a unit cylinder geometry is a good representation of the particles under elastic conditions. This same geometry is used in the finite element-based elastic-plastic model of Bao et al., and reasonably good agreement is obtained between the experimental and predicted yield strengths. A fracture-mechanics model is proposed for predicting the elongation to failure. The model assumes the existence of particle cracks, and criticality is based on the strain required for matrix rupture between cracked particles. The damage criterion of Cockcroft and Latham is utilized, and model predictions are compared to data from different investigations. It is shown that the volume fraction of particles and the work-hardening coefficient of the matrix have a strong influence on the strain to failure. Fracture toughness modeling one again exposes the limitations of existing zero-degree crack-propagation models, such as that of Hahn and Rosenfield, which predict increased toughness with yield strength rather than a decrease, which is observed experimentally. A shear-failure model along a 45-deg direction is proposed for the higher-strength conditions, where concentrated slip bands were observed. The model exhibits the inverse toughness dependence on strength and better correlation to peak-aged (PA) data, but shows poorer agreement with underaged (UA) data. Thus, a transition from zero-degree propagation to 45-deg propagation with increasing strength is suggested. A simplified method for extracting particle stresses is illustrated and is used to estimate a Weibull modulus of 4.9 and a Weibull strength of 2450 MPa for the SiC particles of an average diameter of 10 μm. This article is based on a presentation made in the Symposium “Mechanisms and Mechanics of Composites Fracture” held October 11–15, 1998, at the TMS Fall Meeting in Rosemont, Illinois, under the auspices of the TMS-SMD/ASM-MSCTS Composite Materials Committee.     

The interrelationship of fracture toughness and microstructure in a Ti-5.25Al-5.5V-0.9Fe-0.5Cu alloy

Fracture toughness of anα-Β titanium alloy heat treated to a constant yield strength has been found to depend upon the morphology of α produced or remaining after the initial solution treatment. In equiaxed α structures, fracture toughness depends linearly upon the grain boundary area per unit volume,S _v, and is independent of equiaxed α particle size or spacing. In a grain boundary α structure fracture toughness depends both onS _v and, within limits, linearly on the thickness of the α. Explanations are offered for the observed propagation of cracks at α-@#@ Β interfaces and for the observation that high fracture toughness can accompany low tensile ductility. This paper is based on a thesis to be submitted by M. A. Greenfield in partial fulfillment of the requirements for the Ph.D. degree in metallurgy at New York University.     

Metallurgical factors affecting fracture toughness of aluminum alloys

Crack extension in commercial aluminum alloys proceeds by the “ductile” or fibrous mode. The process involves the large, ~1 μm to ~10μm, Fe-, Si-, and Cu-bearing inclusions which break easily, and the growth of voids at the cracked particles. The linking-up of the voids is accomplished by the rupture of the intervening ligaments, and this is affected by the fine, ~0.01μm precipitate particles that strengthen the matrix. The ~0.1μm Cr-, Mn-, and Zr-rich intermediate particles are more resistant to cracking and may enter the process in the linking-up stage. The fracture toughness of aluminum alloys therefore depends on a) the extent of the heavily strained region ahead of the crack tip, which is a function of the yield strength arad modulus, b) the size of the ligaments which is related tof _c, the volume fraction of cracked particles, and c) the work of rupturing the ligaments. An approximate analysis predicts K_Ic varies asf _c-1/6, and this is in agreement with measurements on alloys with comparable yield strength levels. Studies in which the aging conditions are altered for the samef _cshow that the toughness decreases with increasing yield strength level. This degradation in toughness is related to the localization of plastic deformation. The tendency for localization is illustrated with the help of “plane strain” tension and bend specimens whose behavior is related to the toughness. Measurements of the strain distribution on the microscale show that slip is relatively uniformly distributed in a 7000-type alloy with low inclusion and particle content when the material is in the as-quenched and overaged conditions. In contrast the distribution is highly nonuniform in the peak aged condition where slip is concentrated in widely spaced superbands involving coarse slip bands with large offsets that crack prematurely. The connection between the tendency for slip localization and the fine precipitate particles which strengthen the matrix remains to be established. In overaged alloys grain boundary ruptures occur within the superbands. The amount of intergranular failure increases with grain size and is accompanied by a loss of fracture toughness. This paper is based on an invited presentation made at a symposium on “Advances in the Physical Metallurgy of Aluminum Alloys” held at the Spring Meetings of TMS-IMD in Philadelphia, Pennsylvania, on May 29 to June 1, 1973. The symposium was co-sponsored by the Physical Metallurgy Committee and the Non-Ferrous Metals Committee of TMS-IMD     

Deformation and fracture of a particle-reinforced aluminum alloy composite: Part I. Experiments

Mechanical tests were performed on a powder-metallurgically processed 7093/SiC/15p discontinuously reinforced aluminum (DRA) composite in different heat-treatment conditions, to determine the influence of matrix characteristics on the composite response. The work-hardening exponent and the strain to failure varied inversely to the strength, similar to monolithic Al alloys, and this dependence was independent of the dominant damage mode. The damage consisted of SiC particle cracks, interface and near-interface debonds, and matrix rupture inside intense slip bands. Fracture surfaces revealed particle fracture-dominated damage for most of the heat-treatment conditions, including an overaged (OA) condition that exhibited a combination of precipitates at the interface and a precipitate-free zone (PFZ) in the immediate vicinity. In the highly OA conditions and in a 450°C as-rolled condition, when the composite strength became less than 400 MPa, near-interface matrix rupture became dominant. A combination of a relatively weak matrix and a weak zone around the particle likely contributed to this damage mode over that of particle fracture. Fracture-toughness tests show that it is important to maintain a proper geometry and testing procedure to obtain valid fracture-toughness data. Overaged microstructures did reveal a recovery of fracture toughness as compared to the peak-aged (PA) condition, unlike the lack of toughness recovery reported earlier for a similar 7XXX (Al-Zn-Cu-Mg)—based DRA. The PA material exhibited extensive localization of damage and plasticity. The low toughness of the DRA in this PA condition is explored in detail, using fractography and metallography. The damage and fracture micromechanisms formed the basis for modeling the strength, elongation, toughness, and damage, which are described in Part II of this work. This article is based on a presentation made in the Symposium “Mechanisms and Mechanics of Composites Fracture” held October 11–15, 1998, at the TMS Fall Meeting in Rosemont, Illinois, under the auspices of the TMS-SMD/ASM-MSCTS Composite Materials Committee.     

Stochastic modeling of the independent roles of particle size and grain size in transgranular cleavage fracture

The independent roles of grain size and particle size on sharp crack and rounded notch toughness are investigated over a range of temperatures from the lower shelf into the early ductile/brittle transition region. The results are interpreted in terms of a weakest link statistical model wherein the onset of failure coincides with the critical propagation of a particle microcrack into the matrix. It is shown that, for a fixed particle size distribution, both sharp-crack and rounded-notch toughness decrease with increasing grain size. However, at fixed grain size, the sharp-crack toughness increases, while the rounded-notch toughness decreases with increasing particle size. Such effects result primarily from the difference in the number of activated particles in the plastic zone. Formerly Graduate Student in the Department of Materials Science and Mineral Engineering, University of California, Berkeley. This paper is based on a presentation made at the symposium “Stochastic Aspects of Fracture” held at the 1986 annual AIME meeting in New Orleans, LA, on March 2–6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.     

Deformation and fracture of a particle-reinforced aluminum alloy composite: Part I. Experiments

Mechanical tests were performed on a powder-metallurgically processed 7093/SiC/15p discontinuously reinforced aluminum (DRA) composite in different heat-treatment conditions, to determine the influence of matrix characteristics on the composite response. The work-hardening exponent and the strain to failure varied inversely to the strength, similar to monolithic Al alloys, and this dependence was independent of the dominant damage mode. The damage consisted of SiC particle cracks, interface and near-interface debonds, and matrix rupture inside intense slip bands. Fracture surfaces revealed particle fracture-dominated damage for most of the heat-treatment conditions, including an overaged (OA) condition that exhibited a combination of precipitates at the interface and a precipitate-free zone (PFZ) in the immediate vicinity. In the highly OA conditions and in a 450 °C as-rolled condition, when the composite strength became less than 400 MPa, near-interface matrix rupture became dominant. A combination of a relatively weak matrix and a weak zone around the particle likely contributed to this damage mode over that of particle fracture. Fracture-toughness tests show that it is important to maintain a proper geometry and testing procedure to obtain valid fracture-toughness data. Overaged microstructures did reveal a recovery of fracture toughness as compared to the peak-aged (PA) condition, unlike the lack of toughness recovery reported earlier for a similar 7XXX (Al-Zn-Cu-Mg)-based DRA. The PA material exhibited extensive localization of damage and plasticity. The low toughness of the DRA in this PA condition is explored in detail, using fractography and metallography. The damage and fracture micromechanisms formed the basis for modeling the strength, elongation, toughness, and damage, which are described in Part II of this work. This article is based on a presentation made in the Symposium “Mechanisms and Mechanics of Composites Fracture” held October 11–15, 1998, at the TMS Fall Meeting in Rosemont, Illinois, under the auspices of the TMS-SMD/ASM-MSCTS Composite Materials Committee.     

Influence of particle size and volume percent of flaky mo particles on the mechanical properties of AI2O3/Mo composites

The influence of particle size and volume percent of Mo particles on flake-forming behavior of Mo powders during a ball milling process and three-point flexural strength and fracture toughness of A1₂O₃ composites reinforced with flaky Mo particles have been investigated. The flake-forming behavior of Mo powders mixed with A1₂O₃ powders becomes prominent with increasing Mo particle size, while remaining almost independent of Mo volume percent. The microstructure of the composites reinforced with flaky Mo particles is anisotropic, depending on the arrangement of these Mo particles in the A1₂O₃ matrix. The microdispersion of flaky Mo particles contributes remarkably to an increase in both flexural strength and fracture toughness. The flexural strength increases with decreasing Mo particle size, while the fracture toughness increases with increasing Mo particle size, which corresponds to an increase of the flake-forming tendency of these particles. Furthermore, the flexural strength and fracture toughness can be simultaneously improved by increasing the volume fraction of flaky Mo particles. The microstructural observations indicate that the improvement in strength may be attributed to a grain-refining effect due to inhibition of grain growth of the matrix by the presence of Mo particles. In addition, the improvement in fracture toughness may be due to plastic deformation of Mo particles at a crack tip, which is accelerated more by the flaky rather than the small spherical shape.     

Toughness-strength relations in the overaged 7449 al-based alloy

This article examines the relationship between plane strain fracture toughness, K _Ic , the tensile properties, and the microstructure of the overaged 7449 aluminum-plate alloy, and compares them to the 7150 alloy. The 7449 alloy has a higher content of η′/η precipitates; and, the 7150 alloy contains a greater amount of coarse intermetallic particles, as it contains an appreciable amount of coarse S phase (Al₂CuMg), which is largely absent in the 7449 alloy. The toughness of the alloys shows an increase on overaging, and the 7449 alloy shows a reasonably linear toughness—yield strength relation on extended overaging. Several mechanisms of failure occur: coarse voiding at intermetallics and a combined intergranular/transgranular shear fracture mode, with the former becoming more important as overaging progresses. Drawbacks of existing models for toughness are discussed, and a new model for plane strain fracture toughness, based on the microstructurally dependent work-hardening factor, K _A , introduced in Ashby’s theory of work hardening, is developed. This model predicts a linear relation between K _Ic and K _A ^/0.85 /σ _ys ^/0.35 , where σ _ys is the yield strength, which is consistent with the experimental data.     

Observations on the effect of cementite particles on the fracture toughness of spheroidized carbon steels

The results of experimental studies of the influence of cementite particles on the fracture toughness of a number of spheroidized carbon steels at low temperatures were analyzed in terms of current theories of crack-tip behavior. The fracture toughness parameterK _IC was evaluated by using circumferentially notched and fatigue-cracked cylindrical specimens. The conclusions are summarized as follows: 1) In general,K _IC decreases with increasing volume fraction and increasing size of the carbide particles. 2) Crack initiation occurs at the carbide particles. 3) Crack propagation occurs by cleavage if the stress conditions satisfy the Ritchie, Knott and Rice criterion that a critical cleavage stress is achieved over a minimum microstructural size scale. The critical stress is that required to propagate a crack from a particle and the minimum size scale is of the order of 1 to 2 grain sizes. 4) Crack propagation occurs initially by fibrous rupture if the stress intensification is insufficient to attain the critical cleavage stress. P. Rawal was formerly affiliated.     

Mobility of the β1-γ 1 ′ martensitic interface in Cu-Al-Ni: Part II. Model calculations

The interaction of the twinnedβ _-1-γ ₁ ^′ , martensitic interface with various experimentally observed obstacle particles is analyzed using a specific dislocation model for the interface. The strain interaction of particles with simple shears and tetragonal distortions and their modulus interactions are treated as functions of particle crystallographic orientation, particle position with respect to interfacial intersection, and particle size. Differences from previous predictions of a simple general interface model arise primarily from differences in the assumed interfacial trajectory relative to the particles. The finite-particle calculations indicate that the point-particle approximation is valid for a particle radius less than one-tenth the interfacial twin period. Overall agreement with the experimentally measured interfacial mobility behavior is greatly improved over the previous simple model prediction. The measured athermal component of the driving force for interfacial motion is consistent with the strain and modulus interaction with 2H-phase particles. The activation-energy /driving-force relations obtained from the thermally activated component are reasonably represented by the strain interaction with the fine-scale atomic displacements of the tweed structure.     

Effect of TiN particles and microstructure on fracture toughness in simulated heat-affected zones of a structural steel

Thermally stable TiN particles can effectively pin austenite grain boundaries in weld heat-affected zones (HAZs), thereby improving toughness, but can also act as cleavage initiators. The HAZs simulated in a GLEEBLE 1500 TCS using two peak temperatures (T _p ) and three cooling times (Δ∼ _8/5) have determined the effects of matrix microstructure and TiN particle distribution on the fracture toughness (crack tip opening displacement (CTOD)) of three steels microalloyed with 0.006, 0.045, and 0.1 wt pct Ti. Coarse TiN (0.5 to 6 μm) particles are identified in steels with the two higher levels of Ti, and fine Ti(C, N) (35 to 500 nm) particles were present in all three steels. Large prior austenite grain size caused by higher T _p decreased fracture toughness considerably in steels containing coarse TiN particles but had little effect in their absence. Fracture toughness was largely independent of matrix microstructure in the presence of coarse particles. Cleavage fracture initiation was observed to occur at coarse TiN particles in the samples with a large prior austenite grain size. Alloy thermodynamics have been used to rationalize the influence of Ti content on TiN formation and its size.     

颗粒形状及基体热处理对SiCp/LD2 断裂韧性的影响

对普通SiC颗粒和钝化处理过的SiC颗粒增强LD2铝复合材料的研究表明,颗粒经钝化处理后,几乎去除了很尖锐的部分,使颗粒呈近等轴状,但颗粒的形状对两种热处理态的复合材料(热挤出态和T6态)的断裂韧性K     

Metallurgical factors affecting high strength aluminum alloy production

With the advent of linear elastic fracture mechanics, the detailed effects of processing and microstructure on toughness can be evaluated. The effect of microstructure on plane stress and plane strain fracture toughness is considered in detail together with strength, fatigue behavior and corrosion resistance. It is concluded that second phase particles in all size ranges can influence toughness. Increasing the size and amount of particles or decreasing precipitate coherency all lead to decreases in toughness. Grain structure is also shown to play a prominent role in determining plane stress fracture toughness ; at a given strength level, a fibrous grain structure and the prevention of recrystallization are desirable. The ability to influence fatigue crack propagation by control of processing is more remote though relatively little systematic work has been carried out in this field. Thermomechanical processing is considered to offer another possible route to achieving a desirable balance of toughness, strength and corrosion resistance. This paper is based on an invited presentation made at a symposium on “Advances in the Physical Metallurgy of Aluminum Alloys” held at the Spring Meeting of TMS-IMD in Philadelphia, Pennsylvania, on May 29 to June 1, 1973. The symposium was co-sponsored by the Physical Metallurgy Committee and the Non-Ferrous Metals Committee of TMS-IMD.     

Effects of tensile prestrain on the notch toughness of low-alloy steel

Tensile prestrains of various levels were applied to blank steel specimens. Four-point bend tests of notched specimens at various temperatures revealed an appreciable drop in the notch toughness of the specimens, which experienced 3 pct tensile prestrain. Further prestrains of up to 20 pct had a negligible effect on the notch toughness despite additional increases in the yield strength. Microscopic analyses combined with finite element method (FEM) calculations revealed that the decrease in toughness resulted from a change of the critical event controlling the cleavage fracture. The increase in yield strength provided by prestraining allowed the normal tensile stress at the notch tip to exceed the local fracture stress σ _f for propagating a just-nucleated microcrack. As a result, for the coarsegrained steel with low σ _f tested presently, the critical event was changed from tensile stress-controlled propagation of a nucleated microcrack to plastic strain-controlled nucleation of the microcrack at the notch tip. A reduction of toughness was induced as a result of this. The increase in yield strength provided by decreasing the test temperature acted in the same way.     

Predicting the stress-strain behavior of polycrystalline α-lron containing hard spherical particles

Recent interest in the work hardening of metal crystals containing a dispersion of hard particles has resulted in analytical expressions relating the work hardening to strain, particle diameter, and volume fraction as well as other material parameters. In this study, these models have been used to calculate the tensile stress-strain behavior of polycrystalline α iron containing dispersions of the intermetallic compound Fe₂Ta. The structural characteristics of the Fe-Ta alloys were thoroughly evaluated. The particle morphology was measured for randomness, mean particle diameter, standard deviation of the particle diameter, volume fraction, and planar interparticle spacing. Also, the matrix flow strength, composition, crystallographic randomness, dislocation morphology and grain size were evaluated. It was found that an Orowan type relationship as modified by Ashby satisfactorily described the yield strength as a function of the interparticle spacing and particle diameter. An experimental slope of 11.1 x 10^-5 kg-cm/mm² and a calculated slope of 9.75 x 10^-5 kg-cm/mm² were found. Both the Hart revised FHP work hardening model and Ashby’s model based on the generation of secondary dislocations were in good agreement with the experimental data. Hart’s revised FHP model required the use of empirically obtained values for the particle volume fraction which differed by a factor of 10 from the measured volume fraction and therefore is not suitable for predictive purposes. At tensile strains greater than 5 pct, the work hardening was characteristic of the matrix without particles; therefore, deviation between the experimental and calculated results based on Ashby’s model occurred at large strains. It is hoped that this study represents a step towards applying work hardening models to more complex polycrystalline alloys.     

Effect of size and shape of tungsten particles on dynamic torsional properties in tungsten heavy alloys

The effect of the size and shape of tungsten particles on dynamic torsional properties in tungsten heavy alloys was investigated. Dynamic torsional tests were conducted on seven tungsten alloy specimens, four of which were fabricated by repeated sintering, using a torsional Kolsky bar, and then the test results were compared via microstructure, mechanical properties, adiabatic shear banding, and deformation and fracture mode. The size of tungsten particles and their hardness were increased as sintering temperature and time were increased, thereby deteriorating fracture toughness. The dynamic torsional test results indicated that in the specimens whose tungsten particles were coarse and irregularly shaped, cleavage fracture occurred predominantly with little shear deformation, whereas shear deformation was concentrated into the center of the gage section in the conventionally fabricated specimens. The deformation and fracture behavior of the specimens having coarse tungsten particles correlated well with the observation of the in situ fracture test results, i.e., cleavage crack initiation and propagation. These findings suggested that there would be an appropriate tungsten particle size because the cleavage fracture mode would be beneficial for the “self-sharpening” of the tungsten heavy alloys.     

颗粒形状及基体热处理对SiCp/LD2断裂韧性的影响

对普通ＳｉＣ颗粒和钝化处理过的ＳｉＣ颗粒增强ＬＤ２铝复合材料的研究表明,颗粒经钝化处理后,几乎去除了很尖锐的部分,使颗粒呈近等轴状,但颗粒的形状对两种热处理态的复合材料的断裂性ＫＱ均无影响,而热挤出态的复合材料ＫＱ低于Ｔ６态。     

Ductile-phase toughening and Fatigue-Crack Growth in Nb-Reinforced Molybdenum Disilicide Intermetallic Composites

A study has been made of the role of ductile-phase toughening on the ambient temperature fracture toughness and fatigue-crack propagation behavior of a molybdenum disilicide intermetallicmatrix composite reinforced with 20 vol pct niobium spheres. Using disk-shaped compact DC(T) samples, only moderate improvements (∼24 pct) in fracture toughnessK _lcvalues were found for the composite compared to the unreinforced MoSi₂ matrix material. Moreover, (cyclic) fatigue- crack propagation was seen at stress intensities as low as 75 to 90 pct ofK _Ic, with growth rates displaying a high dependency (∼14) on the applied stress-intensity range. The lack of significant toughening due to the incorporation of ductile Nb particles is associated with an absence of crack/particle interactions. This is attributed to the formation of a weak reaction-layer interface and elastic mismatch stresses at the crack tip between the Nb and MoSi₂, both factors which favor interfacial debonding; moreover, the spherical morphology of Nb phase stabilizes cracking around the particle. Results suggest that increasing the aspect ratio of the distributed Nb rein- forcement phase with attendant interfacial debonding and eliminating possible Nb-phase em- brittlement due to interstitial impurity contamination are critical factors for the successful development of tougher Nb/MoSi₂ structural composites. Formerly with McDonnell Formerly with McDonnell     

SiC particle cracking in powder metallurgy processed aluminum matrix composite materials

Particle cracking is one of the key elements in the fracture process of particulate-reinforced metal-matrix composite (MMC) materials. The present study quantitatively examined the amount of new surface area created by particle cracking and the number fraction of cracked particles in a series of SiC-reinforced aluminum-matrix composite materials. These composite materials were fabricated by liquid-phase sintering and contained 9 vol pct of 23, 63, or 142 μm SiC. The matrix properties were varied by heat treating to either an underaged or peak-aged condition. In general, the new surface area created by particle cracking (S _v ) and the number fraction of cracked particles (F_no) were linearly dependent on the local strain along the tensile specimen. Multiple cracks were frequently observed in the composites containing large particles. It was found that the new surface area created by particle cracking per unit strain was higher for the case of high-strength matrices and was not systematically affected by particle size within the range studied. The number fraction of cracked particles was affected by both particle size and matrix strength. A higher number fraction of particles cracked in the composites reinforced with large particles and with high matrix yield strengths. These results are interpreted in terms of the size of the particle defects, which is a function of particle size, and the critical flaw size necessary to crack a given particle, which is a function of the stress on the particle. The new surface area created by cracking and the fraction of cracked particles were related and are in good agreement for the large and medium sized particles.     

Fracture behaviour of ceramic laminates in bending—I. Modelling of crack propagation

These two papers concern the fracture behaviour of specimens made up of cermic sheets, separated by thin interlayers, which act to deflect cracks and thus to prevent catastrophic failure of the specimen. The treatment is divided into two parts. In this first paper, the behaviour of this type of material during bending is quantitatively modelled, while the second paper compares predictions from the model with experimental data. The model is based on through-thickness cracks propagating when a critical stress is reached and interfacial cracks then advancing a distance dictated by the available energy. The variation in laminae strengths is modelled using a Monte Carlo method to determine the strength of successive laminae for a given Weibull modulus. The model is used to predict load/displacement plots and to explore the effects of changes in loading geometry and specimen variables, including Young's modulus, lamina strength, loading span, interfacial toughness, as well as lamina and sample thickness. A distinction is drawn between the energy actually absorbed in causing complete failure of the specimen as measured from the area under the load/displacement curve, and the amount of energy necessary to cause the crack propagation which occurred. These differ if the energy available to drive the interfacial cracks is more than sufficient for them to reach the ends of the specimen or if energy is dissipated elsewhere in the system. A criterion is derived by which specimens can be designed so as to minimise the difference between these two quantities. The significance of this concept in optimising the toughness of these laminated materials is briefly discussed.