Rheology of carbon nanofiber-reinforced polypropylene

The rheological properties of two different nanocomposite systems consisting in the dispersion of carbon nanofibers (CNFs) in polypropylene are investigated. The nanoreinforced systems were identically prepared with two CNFs that differ only in the length of the fibers being otherwise identical to analyze the effect of fiber aspect ratio. Linear dynamic viscoelasticity and the steady-state rheology of the two different nanocomposites are presented. The system reinforced with CNFs with larger aspect ratio shows several rheological features that resemble peculiarities of rodlike polymers in the nematic liquid crystalline phase.     

On quasi-non-destructive strength and toughness testing of elastic–plastic materials

Non-destructive evaluation of mechanical material properties, like strength and fracture toughness, is impossible for principal reasons. However, there are possibilities of quasi-non-destructive estimation methods, which can be quite useful in practice. Instrumented indentation tests are often suitable to get information about the elastic–plastic behaviour, where the indentation depth is measured as a function of indentation force. By approximate analytical methods, key parameters like ultimate tensile strength, work-hardening exponent or even yield stress can be derived from these measurements. A mobile indenter is presented here and its use in ambulant testing is described. To obtain the uniaxial stress–strain curve more directly and more exactly, the same instrument can be used for a miniature compression test, where a small pin is machined out from the surface of the material. Furthermore, to get information about the toughness of materials, a carving instrument has been developed, which allows the energy required to introduce a defined furrow to be measured and correlated with toughness parameters.     

The roles of toughness and cohesive strength on crack deflection at interfaces

In order to design composites and laminated materials, it is necessary to understand the issues that govern crack deflection and crack penetration at interfaces. Historically, models of crack deflection have been developed using either a strength-based or an energy-based fracture criterion. However, in general, crack propagation depends on both strength and toughness. Therefore, in this paper, crack deflection has been studied using a cohesive-zone model which incorporates both strength and toughness parameters simultaneously. Under appropriate limiting conditions, this model reproduces earlier results that were based on either strength or energy considerations alone. However, the general model reveals a number of interesting results. Of particular note is the apparent absence of any lower bound for the ratio of the substrate to interface toughness to guarantee crack penetration. It appears that, no matter how tough an interface is, crack deflection can always be induced if the strength of the interface is low enough compared to the strength of the substrate. This may be of significance for biological applications where brittle organic matrices can be bonded by relatively tough organic layers. Conversely, it appears that there is a lower bound for the ratio of the substrate strength to interfacial strength, below which penetration is guaranteed no matter how brittle the interface. Finally, it is noted that the effect of modulus mismatch on crack deflection is very sensitive to the mixed-mode failure criterion for the interface, particularly if the cracked layer is much stiffer than the substrate.     

Size effects on strength, toughness and fatigue crack growth of gradient elastic solids

The present study investigates the microstructural size effect on the strength of a bar under axial loading, and on the toughness and crack growth of a beam under three-point bending within the framework of strain gradient elasticity. The gradient responses have been found considerably tougher as compared to the classical theory predictions and the observed deviation increases with increasing values of the non-dimensional parameter g/L (microstructural length over structural length). Based on the analytical solution of the strain energy release rate for the three-point bending case, a new, simple and universal, strain gradient elasticity, brittle fracture criterion and a new, size adjusted fatigue crack growth law have been established. Finally, the analytical predictions of the current modeling compare well with previous experimental data, based on three-point bending tests on single-edge notched concrete beams.     

Optimizing material strength constants numerically extracted from taylor impact data

Advanced design requirements have dictated a need for the mechanical properties of materials at high strain rates. Mechanical testing for these data poses a significant problem for experimentalists. High-speed testing machines have a limited capability at rates approaching 10²/s. The split Hopkinson pressure bar is the most reliable alternative for rates approaching 10⁴/s. Plate impact experiments are capable of generating strain rates of 10⁸/s and higher. The Taylor impact test occupies a place of particular importance by providing data at strain rates on the order of 10⁴/s–10⁵/s. The issue at present is extracting the data. This paper provides a method for obtaining dynamic strength model material constants from a single Taylor impact test. A polynomial response surface is used to describe the volume difference (error) between the deformed specimen from the Taylor test and the results of a computer simulation. The volume difference can be minimized using an optimizer, with the result being an optimum set of material constants. This method was applied to the modified Johnson-Cook model for OFHC copper. Starting from a nominal set of material constants, the iterative process improved the relative volume difference from 23.1 percent to 4.5 percent. Other starting points were used that yielded similar results. The material constants were validated by comparing numerical results with Taylor tests of cylinders having varying aspect ratios, calibers and impact velocities.     

Dynamic fracture toughness of high strength metals under impact loading: increase or decrease

An elusive phenomenon is observed in previous investigations on dynamic fracture that the dynamic fracture toughness(DFT) of high strength metals always increases with the loading rate on the order of TPa.m 1 /2.s 1.For the purpose of verification,variation of DFT with the loading rate for two high strength steels commonly used in the aviation industry,30CrMnSiA and 40Cr,is studied in this work.Results of the experiments are compared,which were conducted on the modified split Hopkinson pressure bar(SHPB) apparatus,with striker velocities ranging from 9.2 to 24.1 m/s and a constant value of 16.3 m/s for 30CrMnSiA and 40Cr,respectively.It is observed that for 30CrMnSiA,the crack tip loading rate increases with the increase of the striker velocity,while the fracture initiation time and the DFT simultaneously decrease.However,in the tests of 40Cr,there is also an increasing tendency of DFT,similar to other reports.Through an in-depth investigation on the relationship between the dynamic stress intensity factor(DSIF) and the loading rate,it is concluded that the generally increasing tendency in previous studies could be false,which is induced from a limited striker velocity domain and the errors existing in the experimental and numerical processes.To disclose the real dependency of DFT on the loading rate,experiments need to be performed in a comparatively large striker velocity range.     

A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates

Free edge delamination in composite structures results from very localised stress fields which induce a stress concentration promoting the nucleation of an interfacial crack. To predict such a delamination onset at the free edge of a $(\pm \theta {)}_s$ laminate in traction, use is made of a strength and toughness criterion which combines a stress condition with an energy analysis. A generalised plane strain model allows to determine the stress distribution near the free edge and the energy released by the nucleation of an interfacial crack. The results show that this approach can predict the delamination onset for $((\pm 10{)}_s\text{,}(\pm 20{)}_s)$ laminates provided the interfacial fracture energy and interlaminar shear strength are known. These characteristic values can be identified with the help of traction tests performed on samples with different thicknesses.     

Balancing strength and toughness of calcium-silicate-hydrate via random nanovoids and particle inclusions: Atomistic modeling and statistical analysis

As the most widely used manufactured material on Earth, concrete poses serious societal and environmental concerns which call for innovative strategies to develop greener concrete with improved strength and toughness, properties that are exclusive in man-made materials. Herein, we focus on calcium silicate hydrate (C-S-H), the major binding phase of all Portland cement concretes, and study how engineering its nanovoids and portlandite particle inclusions can impart a balance of strength, toughness and stiffness. By performing an extensive +600 molecular dynamics simulations coupled with statistical analysis tools, our results provide new evidence of ductile fracture mechanisms in C-S-H – reminiscent of crystalline alloys and ductile metals – decoding the interplay between the crack growth, nanovoid/particle inclusions, and stoichiometry, which dictates the crystalline versus amorphous nature of the underlying matrix. We found that introduction of voids and portlandite particles can significantly increase toughness and ductility, specially in C-S-H with more amorphous matrices, mainly owing to competing mechanisms of crack deflection, voids coalescence, internal necking, accommodation, and geometry alteration of individual voids/particles, which together regulate toughness versus strength. Furthermore, utilizing a comprehensive global sensitivity analysis on random configuration-property relations, we show that the mean diameter of voids/particles is the most critical statistical parameter influencing the mechanical properties of C-S-H, irrespective of stoichiometry or crystalline or amorphous nature of the matrix. This study provides new fundamental insights, design guidelines, and de novo strategies to turn the brittle C-S-H into a ductile material, impacting modern engineering of strong and tough concrete infrastructures and potentially other complex brittle materials.     

Probability distribution of fracture elongation,strength and toughness of notched rectangular blocks with lognormal Young's modulus

We find analytical approximations to the probability distribution of fracture properties of one-dimensional rods and thin two-dimensional plates when Young’s modulus varies spatially as an isotropic lognormal field. The properties considered are the elongation, strength, and toughness modulus at fracture initiation and at ultimate failure. This is an extension of a previous study that, under the same conditions, dealt with the distribution of the bulk elastic moduli (Dimas et al., 2015). For all quantities at fracture initiation our approach is analytical in 1D and semi-analytical in 2D. For ultimate failure, we quantify the random effects of fracture propagation and crack arrest by fitting regression models to simulation data and combine the regressions with the distributions at fracture initiation. The results are validated through a series of Monte Carlo simulations. Through parametric analysis, we gain insight into the strengthening/weakening roles of the Euclidean dimension and size of the specimen and the variance and correlation function of the log-modulus field.     

冻融循环和干湿循环作用下砂岩断裂韧度及其与强度特征相关性的试验研究

以三峡库区岸边坡消落带的典型砂岩为研究对象,针对其实际的赋存环境设计了干湿循环和冻融循环2种试验方案,分别研究了2种试验方案过程中砂岩试样的力学特征,分析了浸泡在不同化学溶液中的砂岩试样经历不同循环次数后各力学参数的变化规律。试验结果表明：干湿循环和冻融循环作用下砂岩试样具有明显的“弱化”趋势,其断裂韧度、抗压强度和抗拉强度劣化趋势基本一致,但试样各力学参数劣化程度却存在差异。其中,断裂韧度KIC的劣化程度最大,抗拉强度次之,抗压强度最小。干湿循环和冻融循环作用过程中砂岩试样各力学参数的劣化程度均非常显著,该现象说明在模拟库岸边坡消落带岩体遭受化学溶液作用时,干湿循环和冻融循环作用均是不可能忽视的影响因素。但比较而言,在冻融循环作用下砂岩试样各力学参数劣化程度更加显著。不同的化学溶液对砂岩试样力学特征的损伤劣化程度的影响有所不同,酸性化学溶液加剧了砂岩的劣化程度,而SO42-离子对砂岩劣化的影响大于HCO3-离子的。     

Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters

A fracture criterion of the type of the Neuber-Novozhilov criterion is proposed to describe the fracture in the vicinity of the tip of a V-shaped notch under tensile and shear loading. In the proposed criterion, the limits of averaging of the stresses along the notch axis depend on the presence, location, and size of the initial defects in the material. The crystal lattice parameter of the initial material is chosen for the characteristic linear size. For a V-shaped notch subjected to tension and shear, simple equations are obtained that relate the stress intensity factors for the modified singularity coefficients, the singularity coefficients themselves, and the theoretical tensile and shear strengths of a single crystal of the material taking into account the damage to the material in the vicinity of the notch tip. The equations obtained allow a passage to the limit from a notch to a crack. It is shown that the classical critical stress intensity factor used in the strength analysis of cracked solids is not a material constant.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 106–115, January–February, 2005.     

不同化学溶液下砂岩I型断裂韧度及其强度参数相关性的试验研究

本文通过长期浸泡的方法,以陕西铜川新区龙潭水库典型的库岸边坡的砂岩为研究对象,研究了浸泡在不同化学溶液下砂岩的力学特性及其损伤劣化机制,分析了经不同化学溶液腐蚀后试样的物理力学特性随化学腐蚀时间的劣化规律。研究发现：化学腐蚀后砂岩的物理力学特性均发生不同程度的劣化,其随化学腐蚀时间的劣化规律基本一致;但不同化学溶液下试样物理力学特性的劣化程度有所差异,酸性溶液（pH=3.0）加剧了砂岩的劣化程度,中性化学溶液对其损伤劣化程度也有一定的影响,试验初期,强碱性溶液下砂岩的劣化程度最小,但随着化学腐蚀时间的加长,强碱性溶液下的劣化程度逐渐加剧,大于中性溶液下的,但仍小于酸性溶液。化学腐蚀后砂岩试样均呈现出明显的弱化趋势,其断裂韧度KIC、抗压强度和抗拉强度的劣化程度显著,但各力学特征的劣化程度存在明显的差异,其中抗压强度的劣化程度相对减小,而其KIC的劣化程度较大;同时,化学腐蚀后砂岩的断裂韧度与抗拉强度、抗压强度间的一致性比较明显,存在明显线性关系。可以利用不同化学溶液下砂岩的裂纹扩展半径r来间接说明其力学特征发生损伤劣化的程度。     

On the toughening of brittle materials by grain bridging: Promoting intergranular fracture through grain angle, strength, and toughness

The structural reliability of many brittle materials such as structural ceramics relies on the occurrence of intergranular, as opposed to transgranular, fracture in order to induce toughening by grain bridging. For a constant grain boundary strength and grain boundary toughness, the current work examines the role of grain strength, grain toughness, and grain angle in promoting intergranular fracture in order to maintain such toughening. Previous studies have illustrated that an intergranular path and the consequent grain bridging process can be partitioned into five distinct regimes, namely: propagate, kink, arrest, stall, and bridge. To determine the validity of the assumed intergranular path, the classical penetration/deflection problem of a crack impinging on an interface is re-examined within a cohesive zone framework for intergranular and transgranular fracture. Results considering both modes of propagation, i.e., a transgranular and intergranular path, reveal that crack-tip shielding is a natural outcome of the cohesive zone approach to fracture. Cohesive zone growth in one mode shields the opposing mode from the stresses required for cohesive zone initiation. Although stable propagation occurs when the required driving force is equivalent to the toughness for either transgranular or intergranular fracture, the mode of propagation depends on the normalized grain strength, normalized grain toughness, and grain angle. For each grain angle, the intersection of single path and multiple path solutions demarcates “strong” grains that increase the macroscopic toughness and “weak” grains that decrease it. The unstable transition to intergranular fracture reveals that an increasing grain toughness requires a growing region of the transgranular cohesive zone be near the cohesive strength. The inability of the body to provide the requisite stress field yields an overdriven and unstable configuration. The current results provide restrictions for the achievement of substantial toughening through intergranular fracture.     

Optimizing diffusion bonding parameters to maximize the strength of AA6061 aluminum and AZ61A magnesium alloy joints

Experimental Techniques - The main difficulty when joining magnesium (Mg) and aluminum (Al) alloys by fusion welding process lies in the existence of oxide films and formation of brittle...     

Fatigue precracking of spin-burst toughness specimens

A hydrostatic pressure-cycling technique developed to permit controlled fatigue precracking of large spin-burst fracture-toughness specimens (disks in excess of 12 in. in diameter and 3 in. long) is described. The procedure involves localized internal-pressure cycling of the specimens by varying the hydrostatic pressure within a small “notched” hole. The technique is capable of generating hydrostatic pressures in excess of 40,000 psi at an operating frequency of one pressure cycle per second. In addition, the cyclic stresses are independent of specimen size, provided thick-wall pressure-vessel conditions exist. An ultrasonic flaw-detection technique used to measure the extent of fatigue-crack growth during cyclic loading is also described. The pertiment data associated with the fatigue precracking of eight alloy steel (σ_ys ≈ 85,000 psi) spin-burst specimens approximately 13 in. in diameter and 10 in. long are presented. The effectiveness of pressure cycling and the accuracy of the crack-monitoring technique are discussed. At a cyclic load range of 8000 to 40,000 psi, fatigue cracks on the order of 0.3 in. long were developed in approximately 60,000 cycles (17 hr). The ultrasonic crack-length-measurement technique was found to exhibit a sensitivity of 0.030 in.     

Dynamic fracture toughness of Homalite-100

Dynamic fracture toughness of Homalite-100 determined by T. Kobayashi and Dally are compared with those previously obtained by the authors where similarities in the two results for single-edged-notch specimens of various configurations are noted. Dynamic fracture toughness of Araldite B obtained by Kalthoff, Beinert and Winkler and those of Homalite-100 obtained by the authors are then compared and, again, similarities in the two results and, in particular, the scatters in experimental data for wedge-loaded DCB specimens of different sizes are found. All three teams of investigators used static near-field solution to compute the dynamic stress-intensity factors from recored dynamic isochromatics or dynamic caustics. Errors generated through this use of static near-field solutions, as well as through the use of larger isochromatic lobes, are thus discussed.     

Fracture toughness evaluation of natural rubber

A method for estimating the fracture toughness of rubber-like materials is presented. Experimental data of a notched natural rubber sheet is analysed by application of the path-independent J-integral. A finite element code for large elastic deformations is used to evaluate the deformed shape of the rubber at crack growth initiation.Discussed is a stability criterion based on the existence of a critical value of J in relation with the experimental results.     

Fracture toughness of open-cell Kelvin foam

Brittle fracture behavior of a perfect open-cell Kelvin foam is considered. The foam is modeled as a spatial lattice consisting of brittle elastic struts rigidly connected to each other at the nodal points. The fracture toughness is determined from the analysis of a quasi-plane problem for a slice of the foam with an embedded finite length crack generated by broken struts. The crack plane is chosen on the basis of a previous study of crack nucleation phenomenon, and the crack length, which assures the self-similar K-field in the tip vicinity, is established by numerical experiments. For the considered densities range the crack includes several hundreds of broken struts and, consequently, the portion of the foam to be considered in the analysis has a very large number of nodal degrees of freedom. The computational cost is reduced significantly by using for the analysis the representative cell method based on the discrete Fourier transform. As a result, the initial problem for the foam slice is reduced to the problem for the repetitive cell which includes 12 struts.