Prediction of the fracture of metals in the processes of cold plastic deformation. Part 1. Approximate model of plastic deformation and fracture of metals

We propose an approximate semiphenomenological model of the joint process of cold plastic deformation and fracture of metals. Within the framework of this model, for 10kp, 20kp, 20G2R, and 38KhGNM steels, we show that moving dislocations overcome barriers through a force process. The formation of nascent microcracks is also realized through a force process, i.e., local stresses in the “head” of an arrested dislocation pileup attain the levels of theoretical strength. We also suggest a general algorithm of the application of the proposed model to the prediction of fracture of metals in technological processes of plastic metal working. Ufa State Aviation Technical University, Ufa, Russia. Translated from Problemy Prochnosti, No. 1, pp. 76–85, January–February, 1999.     

Synthesized theory of plastic deformation depending on the loading rate

The synthesized theory is generalized to take into account the influence of the loading rate on plastic deformation by introducing the integral of inhomogeneity in the formula for the distance to the planes whose motion causes plastic deformation. We take into account the displacements of the planes not only in front of the stress vector but also behind it. The integral of inhomogeneity depends on the history of loading rate, which enables us to describe the processes of hardening, softening, and stabilization and the Bauschinger effect in plastically deformed materials. Technical Institute, Pedagogical University of Bydgoszcz. Bydgoszcz, Poland. “L'vivs'ka Politekhnika” State University, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 1, pp. 39–42, January–February, 2000.     

A new etching technique for revealing the plastic deformation zone in an Al–Cu–Mg alloy

A new etching technique for revealing the plastic deformation zone in an Al–Cu–Mg alloy has been developed. The etching with the proposed etching agent was conducted on the deformed sample after being heated to 673 K for 3 h. With this etching technique, the plastic deformation zone was clearly observed even under low magnification. This was due to the change of microstructural characteristics in the plastic deformation zone after the heating process, in which there is significant precipitation of Al₂Cu and Mg₂Si, caused by the high energy arising from the severe deformation.     

The combined plastic and discrete fracture deformation framework for finite-discrete element methods

The combined finite-discrete element method (FDEM) was originally developed for fracture and fragmentation of brittle materials, more specifically for cementitious and rock-like materials. In this work, a combination of a discrete crack and plastic deformation has been combined and applied to FDEM simulation of fracture. The deformation is described using a FDEM-specific mechanistic approach with plastic deformation being formulated in material embedded coordinate systems leading to multiplicative decomposition and plastic flow, that is, resolved in stretch space; this is combined with the FDEM fracture and fragmentation criteria. The result and main novelty of the present work is a robust framework for simulation of large strain solid deformation combined with a multiplicative decomposition-based model that simultaneously involves elasticity, plasticity, and fracture.     

Influence of preliminary cyclic plastic deformation on crack resistance

The influence of preliminary (before crack origin) cyclic plastic deformation by tension-compression (R = _min/_max = –1 on the brittle fracture resistance of 15Kh2MFA heat resistant steel in two conditions was investigated. The preliminary loading was done at 293 K and the fracture at 123 and 293 K. It was established that in the case of relatively short preliminary deformation the change in static fracture toughness is caused by a change in yield strength as the result of the Bauschinger effect. However, with an increase in cyclic deformation the total irreversibly dispersed specific energy of inelastic deformation and the structural changes in the material are the determining factor. A physically based method is proposed for prediction of the influence of preliminary cyclic plastic deformation on the brittle fracture resistance of cyclically softening steels.Institute of Problems of Strength of the Academy of Sciences of the Ukrainian SSR, Kiev. Leningrad. Translated from Problemy Prochnosti, No. 11, pp. 14–20, November, 1989.     

Geometry and grain size effects on the fracture behavior of sheet metal in micro-scale plastic deformation

The demand on micro-parts is significantly increasing in the last decade due to the trend of product miniaturization. When the part size is scaled down to micro-scale, the billet material consists of only a few grains and the material properties and deformation behaviors are quite different from the conventional ones in macro-scale. The size effect phenomena occur in micro-scale plastic deformation or micro-forming and there are still many unknown phenomena related to size effect, including geometry and grain size effects. It is thus critical to investigate the size effect on deformation behavior, especially for the fracture behavior in micro-scale plastic deformation. In this research, tensile test was conducted with annealed pure copper foils with different thicknesses and grain sizes to study the size effects on fracture behavior. It is found that flow stress, fracture stress and strain, and the number of micro-voids on the fracture surface decrease with the decreasing ratio of specimen size to grain size. Based on the experimental results, dislocation density based models which consider the interactive effect of specimen and grain sizes on fracture stress and strain are developed and their accuracies are further verified and validated with the experimental results obtained from this research and prior arts.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 4. Fracture toughness after plastic prestraining of materials with cracks

The paper presents the results of an experimental investigation of the influence of warm prestressing (WPS) on fracture toughness characteristics of large-size specimens. The WPS has been found to be an efficient method for enhancing brittle fracture resistance of large-size bodies from the investigated materials and can be recommended for practical realization in nuclear reactors and other critical structures whose brittle fracture is impermissible both in the process of normal operation and in emergency situations. The optimum temperature-loading regime of the WPS is defined by both the properties of a given material and its thickness which governs the intensity of plastic deformation in the process of WPS. Based on the established mechanisms of the WPS effect, a physicomechanical model has been developed for the prediction of fracture toughness for pressure-vessel heat-resistant steels after WPS taking into account the influence of the stress state at the crack tip. The model makes it possible to predict fracture toughness for large-size bodies subjected to WPS with the given temperature and loading regimes from the results of testing small laboratory specimens. The most optimum regimes of the WPS can also be determined using this model and even those for several materials making up a structural component and subjected to the WPS. Translated from Problemy Prochnosti, No. 3, pp. 39–54, May–June, 1997.     

High-rate deformation and spall fracture of hadfield steel under action of high-current nanosecond relativistic electron beam

Features of the plastic deformation and dynamic spall fracture of Hadfield steel under conditions of shock wave loading at a straining rate of ∼10⁶ s⁻¹ have been studied. The shock load (∼30 GPa, ∼0.2 μs) was produced by pulses of a SINUS-7 electron accelerator, which generated relativistic electron bunches with an electron energy of up to 1.35 MeV, a duration of 45 ns, and a peak power on the target of 3.4 × 10¹⁰ W/cm². It is established that the spalling proceeds via mixed viscous-brittle intergranular fracture, unlike the cases of quasi-static tensile and impact loading, where viscous transgranular fracture is typical. It is shown that the intergranular character of the spall fracture is caused by the localization of plastic deformation at grain boundaries containing precipitated carbide inclusions.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 3. Brittle fracture

A model has been developed for predicting fracture toughness characteristics on the lower shelf of the fracture toughness temperature dependence considering the influence of specimen dimensions. The model is based on the physicomechanical model of brittle fracture governed by microcleavage critical stress which in its turn depends on plastic prestraining. This model is also based on the assumption that the change in the body dimensions influences fracture toughness as much as the change in the stress state caused by it, which is evaluated by the introduced parameter χ, and affects plastic deformation preceding brittle fracture by cleavage. According to the given model, in some cases an increase in specimen thickness can lead only to a shift of the brittle-to-ductile transition temperature, and in other cases to both a shift of the brittle-to-ductile transition temperature and a decrease in the critical SIF value at which this transition occurs. The paper also presents further elaboration of the probabilistic approach to the prediction of size effect for the cases of brittle fracture based on Weibull's three-parametric distribution. A distinctive feature of this approach is the determination of one of the parameters of the cumulative distribution function, namely, the parameter of location K_{c min} , directly in the experiment and not by conventional statistical methods. This reduces appreciably the requirements for the size of the sample and simplifies the body of mathematics. In this case, the parameter of location K_{c min} corresponds to the critical SIF value during the first unstable jump of a fatigue crack K _fc ⁽¹⁾ which, according to a large number of experimental data, is minimal and the most invariant among all other critical SIF values obtained experimentally. Translated from Problemy Prochnosti, No. 2, pp. 21–31, March–April, 1997.     

Kinetics of scattered fracture in structural metals under elastoplastic deformation

The paper presents a procedure whereby the damage accumulation kinetics in structural materials, such as steel 45, stainless steel 12Kh18N10T, aluminum alloy D16T, and titanium alloy VT22, under elastoplastic deformation is studied based on variation parameters of elastic modulus and resistivity. For complex stress conditions, a continuum model for damage accumulation is proposed which relates the damage parameter to the intensity of accumulated plastic strains. The data calculated by the proposed continuum model are compared to the experimental findings of the investigation of the damage accumulation kinetics for some structural metals. __________ Translated from Problemy Prochnosti, No. 3, pp. 23–34, May–June, 2007.     

Particle fracture and plastic deformation in vanadium pentoxide powders induced by high energy vibrational ball-mill

An X-ray powder profile analysis in vanadium pentoxide powder milled in a high energy vibrational ball-mill for different lengths of time (0–250 h), is presented. The strain and size induced broadening of the Bragg reflection for two different crystallographic directions ([001] and [100]) was determined by Warren-Averbach analysis using a pattern-decomposition method assuming a Pseudo-Voigt function. The deformation process caused a decrease in the crystallite size and a saturation of crystallite size of ∼ 10 nm was reached after severe milling. The initial stages of milling indicated a propensity of size-broadening due to fracture of the powder particles caused by repeated ball-to-powder impact whereas with increasing milling time microstrain broadening was predominant. WA analysis indicated significant plastic strain along with spatial confinement of the internal strain fields in the crystallite interfaces. Significant strain anisotropy was noticed in the different crystallographic directions. A near-isotropy in the crystallite size value was noticed for materials milled for 200 h and beyond. The column-length distribution function obtained from the size Fourier coefficients progressively narrowed down with the milling time.     

Instability of thermal fracture under the conditions of constrained deformation

We study the processes of quasistatic deformation and fracture of brittle materials under the action of rapidly varying temperature fields. As a fracture criterion, we use the condition of attainment of the critical levels of stresses. The analyses of the stressed state and crack growth are performed under the assumptions that the corresponding elements of the stress field are equal to zero on the newly formed free surfaces and that the conditions of the fracture criterion are satisfied at the ends of the crack. It is shown that the process of crack propagation is unstable for the major part of modes of thermomechanical loading: as soon as the critical stresses are attained at a certain point of the body, the crack instantaneously propagates to a critical size corresponding to a new stable state. It is shown that the mechanical overloading of a specimen can substantially weaken the effect of instability of development of the fracture zone. Examples of fracture of elastic brittle bodies are presented. We also perform the numerical analyses of the processes of initiation and propagation of cracks with regard for the plasticity of the material near its heated surface. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 55–60, November–December, 2006.     

Mechanisms of particulate filled polypropylene finite plastic deformation and fracture

The plastic deformation and fracture of aluminium hydroxide filled polypropylene has been investigated. A transition between two mechanisms with an increase of the filler volume fraction has been observed. Below a critical filler volume content φcr ≈ 20 vol% (designated region 1) adhesive failure processes and polymer deformation in the neighbourhoods of different particles occur in an uncorrelated manner. Above this critical value (designated region 2) exfoliation along the surface of the initial portion of inclusions causes the formation of craze-like deformation zones transverse to the direction of the loading. The concentration of craze-like zones is essentially determined by the filler content and the level of interphase interaction which in turn depends on the particle size. In region 1 deformation occurs in a macro heterogeneous way with the formation and growth of a neck. The elongation to break decreases with an increase in the mean diameter of the filler phase. At φ>φcr composites, filled with small particles, fail in quasi brittle manner with the formation of a short and narrow neck. In contrast to the case for a small filler concentration, an increase of the inclusion size leads to an increase in the ultimate elongation and a tendency to macro homogeneous yielding. An explanation of the observed behaviour is proposed based on a change in adhesive failure conditions with filler content and size. This revised version was published online in November 2006 with corrections to the Cover Date.     

Effects of microcrack-damage on fracture behavior of TiAl alloy. Part II: load-controlled tensile test

Specimens of a fully lamellar TiAl alloy and a duplex TiAl alloy were tensile tested using load-controlled procedure. The microcracks were measured for each specimen as it was subjected to various preloading–unloading processes. Loading–unloading–reloading processes of in-situ tensile tests were carried out in a scanning electron microscope (SEM). Effects of microcrack damage on the deformation and fracture behavior were evaluated. The following results of microcrack-damage on deformation and fracture behavior of TiAl alloy were found: (1) The apparent plastic elongation resulted mainly from plastic strain. The elongation caused by microcracks is negligible. (2) No appreciable effects of microcrack damage on the apparent elastic modulus could be found. (3) Microcracks damage produced at higher preloading reduced the fracture stress, however, that produced at lower preloading gave diminished effects.     

Plastic deformation of titanium alloys under simple loading and its mathematical modeling

Results of an experimental investigation of the regularities of plastic deformation of titanium alloys in a plane stress state are analyzed. Tests were performed by loading thin-walled tubular specimens by an axial force and internal pressure under conditions of a proportional increase in the loads. The alloys are found to be transversely isotropic materials whose isotropic surface coincides with the cylindrical surface of the specimen. The process of plastic deformation of the alloys under simple loading is shown to be described well by equations of a previously proposed deformation theory of the plasticity of transversely isotropic media. Translated from Problemy Prochnosti, No. 5, pp. 27–35, September–October, 1999.     

Severe plastic deformation (SPD) and nanostructured materials by machining

Large plastic strains between 1 and 15 can be imposed in chips formed by plane-strain (2-D) machining of metals and alloys. This approach has been used to examine microstructure changes induced by large strain deformation in model systems—copper and its alloys, precipitation-hardenable aluminum alloys, high-strength materials such as titanium, Inconel 718 and 52100 steel, and an amorphous alloy. It is shown that materials with average grain sizes in the range of 60 nm–1 μm can be created by varying the parameters of machining, which in turn affects the deformation processes. Furthermore, a switch-over from an elongated subgrain microstructure to an equi-axed nanocrystalline microstructure, with a preponderance of large-angle grain boundaries, has been demonstrated at the higher levels of strain in several of these materials. This switch-over can be readily controlled by varying the deformation conditions. Dynamic recrystallization has been demonstrated in select material systems under particular conditions of strain and temperature. This study may be seen as providing an important bridge between furthering the understanding of microstructural refinement by large strain deformation and the practical utilization of nanostructured materials in structural and mechanical applications. Conventional plane-strain machining has been shown to be a viable SPD method for examining the underlying processes of very large strain deformation.     

Evolution of deformation domains and kinetics of fatigue fracture of Duralumin polycrystals at the mesoscopic level

Laws governing the buildup of fatigue fracture under cyclic loading of aluminum alloy polycrystals under conditions of multicycle fatigue have been studied by analyzing the spacetime dynamics of mesoscopic structures. It has been shown that under the periodic action of an external mechanical field, deformation domains form in the material at the mesoscopic level. The evolution of these dynamic mesoscopic domain substructures determines the kinetics of the fatigue fracture of the polycrystals. Pis’ma Zh. Tekh. Fiz. 23, 51–57 (December 26, 1997)     

Thickness effect of notched metal sheets on deformation and fracture under tension

The deformation field in notched metal sheets stretched under tension was analysed experimentally. The results of strain distribution were explained by using the result of the near-tip deformation field of non-linear elastic material, combined with a simple model of the plastic state under a mixed plane stress and plane strain condition. Next, the relationship among fracture mechanics parameters, i.e. the notch-tip opening displacement, the notch-tip contraction and $\text{J-}\text{integral}$ was established based on the rigid plastic strip model. Finally, the effect of the specimen thickness on the toughness value at crack initiation and instability was discussed by improving Bluhm's idea that the total fracture resistance was the sum of the fracture work for slant and flat fractures.     

Size effect on deformation behavior and ductile fracture in microforming of pure copper sheets considering free surface roughening

In meso/micro-scaled plastic deformation, material deformation and ductile fracture are quite different from those in macro-scale. The roughness of the free surfaces of workpiece increases with deformation and the decrease of grain number in the sample thickness direction, leading to the nonuniformity of specimen thickness. The so-called size effect and free surface roughening may in turn affect the deformation behavior, ductility and fracture morphology of the samples. To explore the coupled effect of workpiece geometry and grain size on material flow behavior in meso/micro-scaled plastic deformation, uniaxial tensile test of pure copper sheets with different thicknesses and comparable microstructure was performed. The experimental results reveal that the material flow stress, fracture stress and strain, and the number of microvoids on fracture surface are getting smaller with the decreasing ratio of specimen thickness to grain size. In addition, the modified Swift’s equation and the corrected uniform strain are closer to the experimental ones considering the thickness nonuniform coefficient induced by the free surface roughening. Furthermore, the observation of fracture morphologies confirms that the local deformation caused by the free surface roughening leads to strain localization and a decreased fracture strain when there are only a few grains involved in plastic deformation.     

Localization of plastic deformation and fracture in aluminum polycrystals

The effect of the grain size as a basic structural parameter on plastic strain macrolocalization has been studied for polycrystalline aluminum. The mathematical form of the above dependence has been verified. The limiting cases have been defined both for small-and coarse-grain ranges. The effect of sample dimension on the macrolocalization period has been considered. __________ Translated from Problemy Prochnosti, No. 1, pp. 52–55, January–February, 2008.