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1.
The homogenized response of metal matrix composites(MMC) is studied using strain gradient plasticity.The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free energy inside the micro structure is included due to the elastic strains and plastic strain gradients. A unit cell containing a circular elastic fiber is analyzed under macroscopic simple shear in addition to transverse and longitudinal loading. The analyses are carried out under generalized plane strain condition. Micro-macro homogenization is performed observing the Hill-Mandel energy condition,and overall loading is considered such that the homogenized higher order terms vanish. The results highlight the intrinsic size-effects as well as the effect of fiber volume fraction on the overall response curves, plastic strain distributions and homogenized yield surfaces under different loading conditions. It is concluded that composites with smaller reinforcement size have larger initial yield surfaces and furthermore,they exhibit more kinematic hardening. 相似文献
2.
《European Journal of Mechanics - A/Solids》2001,20(4):601-613
For a metal reinforced by aligned short fibres the effect of a material length scale characterising the inelastic deformations of the metal is studied. The elastic-plastic constitutive relations used here to represent the nonlocal effects are formulated so that the instantaneous hardening moduli depend on the gradient of the effective plastic strain. Numerical cell-model analyses are used to obtain a parametric understanding of the influence of different combinations of the main material parameters. The analyses show a strong dependence on the fibre diameter for given values of all other material parameters, and it is shown that this dependence differs somewhat for different values of the fibre aspect ratio. 相似文献
3.
A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used.
An elastic-power law hardening strain gradient material is considered and two hardening laws, i. e. a separation law and an
integration law are used respectively. As for the material with the separation law hardening, the angular distributions of
stresses are consistent with the HRR field, which differs from the stress results[19]; the angular distributions of couple stresses are the same as the couple stress results[19]. For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously,
which is the same as the conclusion[19], but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple
stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the
increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient
of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in
another paper.
Supported by the National Science Foundation of China (No. 19704100), Science Foundation of Chinese Academy of Sciences (Project
KJ951-1-20), CAS K. C. Wong Post-doctoral Research Award Fund and the Post Doctoral Science Fund of China. 相似文献
4.
Strain gradient effects on cyclic plasticity 总被引:1,自引:0,他引:1
Christian F. Niordson Brian Nyvang Legarth 《Journal of the mechanics and physics of solids》2010,58(4):542-557
Size effects on the cyclic shear response are studied numerically using a recent higher order strain gradient visco-plasticity theory accounting for both dissipative and energetic gradient hardening. Numerical investigations of the response under cyclic pure shear and shear of a finite slab between rigid platens have been carried out, using the finite element method. It is shown for elastic-perfectly plastic solids how dissipative gradient effects lead to increased yield strength, whereas energetic gradient contributions lead to increased hardening as well as a Bauschinger effect. For linearly hardening materials it is quantified how dissipative and energetic gradient effects promote hardening above that of conventional predictions. Usually, increased hardening is attributed to energetic gradient effects, but here it is found that also dissipative gradient effects lead to additional hardening in the presence of conventional material hardening. Furthermore, it is shown that dissipative gradient effects can lead to both an increase and a decrease in the dissipation per load cycle depending on the magnitude of the dissipative length parameter, whereas energetic gradient effects lead to decreasing dissipation for increasing energetic length parameter. For dissipative gradient effects it is found that dissipation has a maximum value for some none zero value of the material length parameter, which depends on the magnitude of the deformation cycles. 相似文献
5.
A solution for the finite-domain Eshelby-type inclusion problem of a finite elastic body containing an anti-plane strain inclusion of arbitrary cross-sectional shape prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). The formulation is facilitated by an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET and suitable for anti-plane strain problems. The disturbed displacement field is obtained in terms of the SSGET-based Green’s function for an infinite anti-plane strain elastic body. The solution reduces to that of the infinite-domain anti-plane strain inclusion problem when the boundary effect is not considered. The problem of a circular cylindrical inclusion embedded concentrically in a finite cylindrical elastic matrix undergoing anti-plane strain deformations is analytically solved by applying the general solution, with the Eshelby tensor and its average over the circular cross section of the inclusion obtained in closed forms. This Eshelby tensor, being dependent on the position, inclusion size, matrix size, and a material length scale parameter, captures the inclusion size and boundary effects, unlike existing ones. It reduces to the classical linear elasticity-based Eshelby tensor for the circular cylindrical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is small and that the boundary effect can dominate when the inclusion volume fraction is high. However, the inclusion size effect is diminishing with the increase of the inclusion size, and the boundary effect is vanishing as the inclusion volume fraction becomes sufficiently low. 相似文献
6.
Christian F. Niordson 《Journal of the mechanics and physics of solids》2003,51(10):1863-1883
A metal reinforced by fibers in the micron range is studied using the strain gradient plasticity theory of Fleck and Hutchinson (J. Mech. Phys. Solids 49 (2001) 2245). Cell-model analyses are used to study the influence of the material length parameters numerically, for both a single parameter version and the multiparameter theory, and significant differences between the predictions of the two models are reported. It is shown that modeling fiber elasticity is important when using the present theories. A significant stiffening effect when compared to conventional models is predicted, which is a result of a significant decrease in the level of plastic strain. Moreover, it is shown that the relative stiffening effect increases with fiber volume fraction. The higher-order nature of the theories allows for different higher-order boundary conditions at the fiber-matrix interface, and these boundary conditions are found to be of importance. Furthermore, the influence of the material length parameters on the stresses along the interface between the fiber and the matrix material is discussed, as well as the stresses within the elastic fiber which are of importance for fiber breakage. 相似文献
7.
A displacement-based finite element-based numerical approach has been employed to study the damage growth in a unidirectional SiC/Al composite containing a pre-existing crack along the fibre/matrix interface. The composite is modeled as a two-material cylinder subjected to uniform displacement. A detailed analysis is made for the stress field in the vicinity of the debond crack tip. This approach incorporates an elastic-plastic analysis combined with a strain energy density criterion to predict debonded crack growth direction, extended stable growth and final termination. The influence of contact taking place between the debonded surfaces is also considered. It is shown that such surface contact leads to reduced stress and strain fields around the crack tip, while the extent of reduction is increased with debonding length. By combining the reduced stress field with the strain energy density criterion, a limiting value for the debonding extension can be calculated for the critical applied displacement that led to fibre fracture. 相似文献
8.
In metal grains one of the most important failure mechanisms involves shear band localization. As the band width is small, the deformations are affected by material length scales. To study localization in single grains a rate-dependent crystal plasticity formulation for finite strains is presented for metals described by the reformulated Fleck–Hutchinson strain gradient plasticity theory. The theory is implemented numerically within a finite element framework using slip rate increments and displacement increments as state variables. The formulation reduces to the classical crystal plasticity theory in the absence of strain gradients. The model is used to study the effect of an internal material length scale on the localization of plastic flow in shear bands in a single crystal under plane strain tension. It is shown that the mesh sensitivity is removed when using the nonlocal material model considered. Furthermore, it is illustrated how different hardening functions affect the formation of shear bands. 相似文献
9.
Per Fredriksson Peter Gudmundson Lars Pilgaard Mikkelsen 《International Journal of Solids and Structures》2009,46(22-23):3977-3987
A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories. 相似文献
10.
《International Journal of Solids and Structures》2003,40(25):6957-6967
A numerical analysis is carried out for the development of damage by fibre–matrix debonding in aluminium reinforced by aligned, short SiC fibres. A unit cell-model that has earlier been applied to study materials with arrays of transversely staggered fibres is here extended to contain a number of differently shaped fibres or particulates in each unit cell, thus representing debonding of a relatively long discontinuous fibre among particulates that do not debond. Interfacial failure is modelled in terms of a cohesive zone model that accounts for decohesion by normal separation as well as by tangential separation. It is found that the evolution of failure can depend rather strongly on the distribution of particulates around a fibre subject to debonding. 相似文献
11.
The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain
gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental
version of the conventionalJ
2 deformation theory. No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones
are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent
modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary
value problem is the same as that in the conventional theory. Two typical crack problems are studied: (a) the crack tip field
under the small scale yielding condition induced by a linear elastic mode-IK-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level
near the crack tip with strain gradient effects is considerable higher than that in the classical theory. The singularity
of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field
is slightly greater than it. Consequently, theJ-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.
The project supported by the National Natural Science Foundation of China (19704100 and 10202023) and the Natural Science
Foundation of Chinese Academy of Sciences (KJ951-1-20) 相似文献
12.
The strain gradient work hardening is important in micro-indentation of bulk metals and thin metallic films, though the indentation of thin films may display very different behavior from that of bulk metals. We use the conventional theory of mechanism-based strain gradient plasticity (CMSG) to study the indentation of a hard tungsten film on soft aluminum substrate, and find good agreement with experiments. The effect of friction stress (intrinsic lattice resistance), which is important in body-center-cubic tungsten, is accounted for. We also extend CMSG to a finite deformation theory since the indentation depth in experiments can be as large as the film thickness. Contrary to indentation of bulk metals or soft metallic films on hard substrate, the micro-indentation hardness of a hard tungsten film on soft aluminum substrate decreases monotonically with the increasing depth of indentation, and it never approaches a constant (macroscopic hardness). It is also shown that the strain gradient effect in the soft aluminum substrate is insignificant, but that in the hard tungsten thin film is important in shallow indentation. The strain gradient effect in tungsten, however, disappears rapidly as the indentation depth increases because the intrinsic material length in tungsten is rather small. 相似文献
13.
The residual strength of a cracked unidirectional fiver reinforced metal matrix composite is studied. We propose a bridging model based on the Dugdale strip yielding zones in the matrix ahead of the crack tips that accounts for ductile deformations of the matrix and fiber debonding and pull-out in the strip yielding zone. The bridging model is used to study the fracture of an anisotropic material and its residual strength is calculated numerically. The predicted results for a SiC/titanium composite agree well with the existing experimental data. It is found that a higher fiber bridging stress and a larger fiber pull-out length significantly contribute to the composite's residual strength. The composite's strength may be more notch-insensitive than the corresponding matrix material's strength depending on several factors such as fiber-matrix interface properties and the ratio of the matrix modulus to an ‘effective modulus’ of the composite. 相似文献
14.
15.
16.
A method for carrying out strain partition under load is described. An ultrasonic device and a suitable extensometer are used
simultaneously. Applied to a ceramic matrix composite, it allows one to evaluate the contribution of the various damage mechanisms
on its highly nonlinear behavior. 相似文献
17.
18.
19.
Castrenze Polizzotto 《International Journal of Solids and Structures》2010,47(1):100-112
Within the framework of isotropic strain gradient plasticity, a rate-independent constitutive model exhibiting size dependent hardening is formulated and discussed with particular concern to its strengthening behavior. The latter is modelled as a (fictitious) isotropic hardening featured by a potential which is a positively degree-one homogeneous function of the effective plastic strain and its gradient. This potential leads to a strengthening law in which the strengthening stress, i.e. the increase of the plastically undeformed material initial yield stress, is related to the effective plastic strain through a second order PDE and related higher order boundary conditions. The plasticity flow laws, with the role there played by the strengthening stress, are addressed and shown to admit a maximum dissipation principle. For an idealized elastic perfectly plastic material with strengthening effects, the plastic collapse load problem of a micro/nano scale structure is addressed and its basic features under the light of classical plastic limit analysis are pointed out. It is found that the conceptual framework of classical limit analysis, including the notion of rigid-plastic behavior, remains valid. The lower bound and upper bound theorems of classical limit analysis are extended to strengthening materials. A static-type maximum principle and a kinematic-type minimum principle, consequences of the lower and upper bound theorems, respectively, are each independently shown to solve the collapse load problem. These principles coincide with their respective classical counterparts in the case of simple material. Comparisons with existing theories are provided. An application of this nonclassical plastic limit analysis to a simple shear model is also presented, in which the plastic collapse load is shown to increase with the decreasing sample size (Hall–Petch size effects). 相似文献
20.
《International Journal of Solids and Structures》2002,39(5):1241-1257
In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom ωi are introduced in addition to the conventional three translational degrees of freedom ui. ωi is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l1. Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. 相似文献