Effect Of Void Size Research Articles

Evaluation of an Infrared Camera Technique for Detecting Mechanically Induced Internal Voids in Syzygium grande

In order to evaluate a proposed tree diagnostic technique employing infrared cameras, research was conducted to evaluate the effect of internal voids on surface temperature using a thermal photographic instrument. Three axial cylindrical voids of increasing size (Void A, 327 cm3; Void B, 745 cm3; Void C, 1159 cm3) were introduced mechanically in 45 cm long stem sections and exposed to direct sunlight. Subsequently, infrared images were collected from two diametrically opposed sides of the stem sections at regular 30-minute intervals over 150 minutes. The collected images were evaluated visually to compare stem features with observed temperature anomalies, and temperature data was extracted from a vertical transect in the infrared images. The data extracted were compared against a control stem section without defects to determine the independent and combined effects of void size and internal position on surface temperature. Mean relative temperature revealed a significant temperature change in the stems containing mechanical voids compared to the control stem. Significant increases in mean relative temperature were recorded on the stems containing Void A and Void B compared to the control. However, there was no significant change in mean relative temperature on the stem section containing Void C.

Microscopic Mechanism Analysis and Experimental Study of Void Beneath Slab

The main cause of cement concrete pavement fracture is void beneath slab, while water is an important factor of void beneath slab. In order to clearly understand impact of water on void beneath cement concrete pavement, this paper analyzes penetration soaking role and scouring of water and studies the evolution process of void under slab. It is founded that the erosion of the grassroots and void beneath the plate influence each other. Conducting a Small-size simulation test by using Falling Weight Deflectometer (FWD), the movement condition of the water in empty area under concrete road and the effect of void size on current scour are got under the action of moving load.

Effects of void size, density, and arrangement on deflagration and detonation sensitivity of a reactive empirical bond order high explosive

The shock response of two-dimensional model high explosive crystals with various arrangements of circular voids is explored. We simulate a piston impact using molecular-dynamics simulations with a reactive empirical bond order model potential for a submicron, subnanosecond exothermic reaction in a diatomic molecular solid. Voids of radius 10 nm reduce the minimum initiating velocity by a factor of 4; a single 2.5 nm void (per periodic image) reduces the minimum velocity for detonation by 10% and the exponent of the induction time's pressure dependence by about 4. In square lattices of voids all of one size, reducing that size or increasing the porosity while holding the other parameter fixed causes the hotspots to consume the material more quickly and detonation to occur sooner and at lower piston velocities. The early time behavior is seen to follow a very simple ignition and growth model. The hotspots collectively develop a broad pressure wave (a sonic, diffuse deflagration front) that, upon merging with the lead shock, transforms it into a detonation. The reaction yields produced by triangular lattices are not significantly different. With random void arrangements, the mean time to detonation is 15.5% larger than with the square lattice; the standard deviation of detonation delays is just 5.1%.

Analysis of current-driven motion of morphologically stable voids in metallic thin films: Steady and time-periodic states

We report results of self-consistent numerical simulations of current-induced migration of morphologically stable voids in metallic thin films accounting rigorously for current crowding, surface curvature, and surface diffusional anisotropy effects. In a previous study, we demonstrated that as the morphological stability limit is approached, the migration speed of a morphologically stable steady void deviates substantially from being inversely proportional to the void size. We also derived a scaling relationship for the void migration speed, rescaled properly with a shape factor, as a function of the void size as described by Cho et al. [Appl. Phys. Lett. 85, 2214 (2004)]. In this study, we calculate accurately shape factors for stable steady void morphologies, as well as for stable time-periodic void morphologies with surface waves propagating on the voids. We predict the effects of surface diffusional anisotropy strength on the migration of stable steady voids, as well as the effects of void size on void migration speed for both steady and time-periodic states. The results validate fully our scaling theory for the current-driven migration of morphologically stable voids and establish its universality. This theory provides an enabling tool for better design of interconnects in integrated circuits toward optimal reliability under conditions that render void migration an important source of metallic thin-film failure.

Size effects on void growth in single crystals with distributed voids

The effect of void size on void growth in single crystals with uniformly distributed cylindrical voids is studied numerically using a finite deformation strain gradient crystal plasticity theory with an intrinsic length parameter. A plane strain cell model is analyzed for a single crystal with three in-plane slip systems. It is observed that small voids allow much larger overall stress levels than larger voids for all the stress triaxialities considered. The amount of void growth is found to be suppressed for smaller voids at low stress triaxialities. Significant differences are observed in the distribution of slips and on the shape of the deformed voids for different void sizes. Furthermore, the orientation of the crystalline lattice is found to have a pronounced effect on the results, especially for the smaller void sizes.

Strain gradient crystal plasticity analysis of a single crystal containing a cylindrical void

The effects of void size and hardening in a hexagonal close-packed single crystal containing a cylindrical void loaded by a far-field equibiaxial tensile stress under plane strain conditions are studied. The crystal has three in-plane slip systems oriented at the angle 60° with respect to one another. Finite element simulations are performed using a strain gradient crystal plasticity formulation with an intrinsic length scale parameter in a non-local strain gradient constitutive framework. For a vanishing length scale parameter the non-local formulation reduces to a local crystal plasticity formulation. The stress and deformation fields obtained with a local non-hardening constitutive formulation are compared to those obtained from a local hardening formulation and to those from a non-local formulation. Compared to the case of the non-hardening local constitutive formulation, it is shown that a local theory with hardening has only minor effects on the deformation field around the void, whereas a significant difference is obtained with the non-local constitutive relation. Finally, it is shown that the applied stress state required to activate plastic deformation at the void is up to three times higher for smaller void sizes than for larger void sizes in the non-local material.

Simulation of Void Collapse in an Energetic Material, Part 2: Reactive Case

In Part 1 a numerical methodology was used to study collapse of voids in energetic materials by ignoring the contributions of the gas phase and chemical reaction. In this paper, the thermomechanical response of solid phase is combined with the vapor-phase compression and chemical reactions to study their effects on the energy deposition mechanisms. The formulation and numerical treatment of the coupled solid-gas interactions, including heat release caused by chemical reactions, are discussed. The effects of loading intensity and void size are studied. The results show that for the micron-size voids under consideration significant gas-phase chemical reactions occur. However, their influence on the void collapse itself is minimal. Results indicate that when voids completely collapse a significant amount of reaction products are created, but the collapse time is too short to set up thermal runaway at the hot spot before void collapse.

RVE-based studies on the coupled effects of void size and void shape on yield behavior and void growth at micron scales

The present paper extends the Gurson and GLD models [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth, Part I—yield criteria and flow rules for porous ductile media. J. Mech. Phys. Solids 99, 2–15; Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Technol. 116, 290–297] to involve the coupled effects of void size and void shape on the macroscopic yield behavior of non-linear porous materials and on the void growth. A spheroidal representative volume element (RVE) under a remote axisymmetric homogenous strain boundary condition is carefully analyzed. A wide range of void aspect ratios covering the oblate spheroidal, spherical and prolate spheroidal void are taken into account to reflect the shape effect. The size effect is captured by the Fleck–Hutchinson phenomenological strain gradient plasticity theory [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advance in Applied Mechanics, vol. 33, Academic Press, New York, pp. 295–361]. A new size-dependent damage model like the Gurson and GLD models is developed based on the traditional minimum plasticity potential principle. Consequently, the coupled effects of void size and void shape on yield behavior of porous materials and void growth are discussed in detail. The results indicate that the void shape effect on the yield behavior of porous materials and on the void growth can be modified dramatically by the void size effect and vice versa. The applied stress triaxiality plays an important role in these coupled effects. Moreover, there exists a cut-off void radius r c, which depends only on the intrinsic length l 1 associated with the stretch strain gradient. Voids of effective radius smaller than the critical radius r c are less susceptible to grow. These findings are helpful to our further understanding to some impenetrable micrographs of the ductile fracture surfaces.

The effect of die attach voiding on the thermal resistance of chip level packages

The presence of voids in the die bond region is known to adversely affect the thermal resistance of the packaged chip-level device. Unfortunately, such voids are easily formed in the solder layer during manufacturing, and are found to nucleate, grow and coalesce with thermal cycling. Although the relationship between package thermal resistance and voids has been examined extensively, little data exist concerning the precise effects of void size, configuration and position. The present study allows the experimental investigation of these effects through application of an innovative experimental technique that carefully controls void geometry and distribution. The results show that for small, random voids, the thermal resistance, θ jc , increases linearly with void volume percentage, V %, according to the equation θ jc = 0.007 V + 1.4987, and for large, contiguous voids the increase follows the exponential relationship, θ jc = 1.427e 0.015 V . At 73% voiding, θ jc was found to increase 30% and 200% for random and contiguous voids, respectively.

Coupling effects of void size and void shape on the growth of prolate ellipsoidal microvoid

The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn: the growth rate of the void with radius smaller than a critical radius r c may be ignored. It is interesting that r c is a material constant independent of the initial void shape and the remote stress triaxiality.

Combined effects of void shape and void size – oblate spheroidal microvoid embedded in infinite non-linear solid

A boundary value problem about the macroscopic response of an infinite material block containing an isolated oblate spheroidal microvoid is investigated by using a Ritz procedure. Special attention is paid to the combined effects of void size and shape on the void evolution. A wide range of void aspect ratio is covered to reflect the shape effect, and the Fleck–Hutchinson phenomenological strain gradient plasticity theory is adopted to capture the scale-dependent behavior of matrix material [Adv. Appl. Mech. 33 (1997) 295]. The void size effect comes into play through the characteristic length ratio λ= l/ r *, where l is the intrinsic material length on the order of microns and r * the equivalent radius. Based on detailed theoretical analyses and numerous numerical calculations, some interesting results are obtained: (1) the influences of the void size and the void shape on the responses of porous material are coupled together. This coupling mainly depends on the remote stress triaxiality applied. The influence of void shape on the void size effect at lower stress triaxiality level is much more significant than that at higher stress triaxiality level; (2) due to the void size effect, the growth rate of the microvoid can be markedly cut down with the void size decreasing. There exists a void critical radius r c. When the void equivalent radius r is close to or smaller than the critical radius, the growth rate of the void is essentially eliminated. The void critical radius r c, which is insensitive to the initial void shape μ 0 and the applied remote stress triaxiality R σ , approximates to the material intrinsic length l 1=0.25∼1 μ m associated with the stretch gradient; (3) besides the remote stress triaxiality level and the void initial shape, the void size also has great influences on the evolution of void shape. These results are significant to understand the evolutions of microvoid on the order of micron or sub-micron.

Vapor pressure and void size effects on failure of a constrained ductile film

To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth. A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.

Effects of void size and gas content on electrical breakdown in lightweight, mechanically compliant, void-filled dielectrics

Dielectric potting materials (encapsulants) are used to prevent air breakdown in high-voltage electrical devices. We report breakdown strengths in void-filled encapsulants, stressed with unipolar voltage pulses of the order of 10 μs duration. High strengths, on the order of 100 kV mm−1, are measured under these test conditions. The materials studied include low-density open celled gel-derived foams with cell sizes of 4 μm or less, closed celled CO2-blown polystyrene and urethane foams, and epoxies containing 48 vol % of hollow glass microballoon (GMB) fillers. These last specimens varied the void gas (N2 or SO2) and also the void diameters (tens to hundreds of μm). Our measurements are thought to be directly sensitive to the rate of field-induced ionization events in the void gas; however, the breakdown strengths of the materials tested appeared to vary in direct proportion with the conventional Paschen-law gas-discharge inception threshold, the electric stress at which gas-ionization avalanches become possible. The GMB-epoxy specimens displayed this type of dependence of breakdown strength on the void-gas density and void size, but the measurements were an order of magnitude above the conventional predictions. Small-celled foams also showed increased breakdown strengths with decreased cell size, although their irregular void geometry prevented a direct comparison with the more uniformly structured microballoon-filled encapsulants. The experimental observations are consistent with a breakdown mechanism in which the discharge of a few voids can launch a full breakdown in the composite material.

Damage and size effect during superplastic deformation

Abstract Superplastic forming is a valuable metal working technique because of the extreme ductility that can be achieved. However, it is limited in application due to the presence of small voids that grow and coalesce during the forming process, often causing premature failure. In order to understand and control this phenomenon accurate constitutive models must be developed which account for void parameters that affect the macroscopic behavior of the material. This paper looks specifically at the effect of void size and spacing on the ductility and flow stress of viscoplastic materials. Based on the gradient-dependent theory of plasticity, a model is proposed that accounts for size effects by incorporating strain gradient terms into a continuum based constitutive equation. Both experimental testing and finite element (FE) modeling were performed on Pb–Sn, tensile specimens with small holes drilled in them in random patterns. The experimental tests indicate that a decrease in void size results in an increase in ductility. The FE results demonstrate that the gradient terms strengthen the material by diffusing the strain in areas of high strain concentration and delay failure by slowing void growth. In addition, the model predicted an increase in ductility and flow stress with decreasing void size.

A note on the effect of surface energy and void size to void growth

Recent studies revealed that rapid void growth is the dominant failure mechanism in an elasto-plastic solid under high mean tensile stress. This paper studies the effect of the surface energy and void size to the void growth. The models of a thick spherical shell and a thick spherical column in void growth are analyzed and numerically estimated. The main conclusion from this study is that, for typical metals, the surface energy effect is negligible for voids larger than 100 nm in size, but it may become significant when the void size is on the order of 10 nm.

A phenomenological theory for strain gradient effects in plasticity

A Strain Gradient Theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations. The strain gradient theory fits within the general framework of couple stress theory and involves a single material length scale l. Minimum principles are developed for both deformation and flow theory versions of the theory which in the limit of vanishing l, reduce to their conventional counterparts: J 2 deformation and J 2 flow theory. The strain gradient theory is used to calculate the size effect associated with macroscopic strengthening due to a dilute concentration of bonded rigid particles; similarly, predictions are given for the effect of void size upon the macroscopibic softening due to a dilute concentration of voids. Constitutive potentials are derived for this purpose.

The effect of void size on the resistivity of sintered tungsten

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Effects of maximum void size and aggregate characteristics on the strength of mortar

The effects of the maximum void size and aggregate shape and roughness on the flexural strength of high strength mortar were investigated. Substantial reductions in the maximum void size and air content of quartz aggregate mortars resulted in flexural strength increases. These increases in flexural strength were somewhat lower than predicted by Griffith's theory, thus suggesting that the maximum void size did not act as the critical flaw controlling the flexural strength. Factors relating to the cement-aggregate bond, including aggregate shape and roughness, appeared to affect the flexural strength more than the maximum void size.

The effect of void size and distribution on ductile fracture

The ductility of materials with different distributions of voids is examined theoretically. The theory of Thomason [7] is used which assumes that the material deforms homogeneously until localized deformation between the voids intervenes. The fracture is expected to occur so rapidly after the onset of localized deformation that the transition from homogeneous to inhomogeneous deformation is used as a criterion for ductility. Upper bound solutions are used to derive a criterion for the fracture strain. Void size distributions with equal numbers of voids of two sizes are examined. It is also investigated how a distribution of inter void distances influences the ductility. The importance of small secondary voids in a distribution of large primary voids is studied. The effect of the shape of the voids is also considered. In all cases analytical expressions are derived for the fracture strain. The void distributions are centered on a plane orthogonal to the tensile axis and all voids are of rectangular shape.