Size effect on the fiber strength of composite pressure vessels

In this study, experimental tests and an analytical approach are conducted to verify the size effect on the fiber strength of a composite pressure vessel. As an analytical method, the Weibull weakest link model and the sequential multi-step failure model are considered and mutually compared. In the case of carbon fiber tensile strength, there is no large difference between the analytical methods for the volumetric size effect. To verify the validity of the analytical approach, experimental tests were performed using fiber strand specimens, unidirectional laminate specimens and composite pressure vessels. Good agreement for fiber strength distribution was shown between the test data and predicted results. The volumetric size effect shows the clearly observed tendency towards fiber strength degradation with increasing stressed volume. Because the volumetric size effect depends on material and processing factors, the reduction of fiber strength due to the stressed volume shows different values according to the variation of material and processing conditions.     

Experiments on concrete under uniaxial impact tensile loading

A problem of practical importance for designing of structural elements is discussed in this paper—the behaviour of concrete subjected to uniaxial impact tensile loading. The “Split Hopkinson Bar” technique was adopted for testing concrete in uniaxial tension at stress rates between 2 and 60 N/mm²/ms. A remarkable increase in tensile strength was observed due to high stress rate. The ratio of impact and static tensile strength varied between 1.33 and 2.34 for various concrete mixes. The influence of maximum aggregate size, water-cement ratio, cement content, cement type and quality, specimen humidity, static compressive strength and loading/casting direction upon the uniaxial impact tensile strength was studied. The high stress rate resulted in an increase of the modulus of elasticity of concrete in uniaxial tension. An explanation for the observed phenomena is suggested.     

The Effect of Size on the Splitting Strength of Cubic Concrete Members

In the study of concrete fractures, split‐tension specimens, such as cylinders, cubes and diagonal cubes, are frequently preferred to beams. However, experimental investigations on concrete reveal that for the same specimen geometry, the nominal strength of specimen decreases with increasing specimen size. This phenomenon is named as the size effect in the fracture mechanics of concrete. Although nominal strength is also highly affected by the width of the distributed load in the split‐tension cylinder and cube specimens, this effect can be negligible within the practical range of the load‐distributed width in the diagonal cubes. However, the number of theoretical and experimental studies with diagonal split‐tension specimens is limited. Besides, a size effect formula for estimating the split‐tensile strength of the diagonal cube specimens has not been proposed. In this study, nine series of cube and diagonal cube specimens, with three different sizes but similar geometries, were tested under different load‐distributed widths. The ultimate loads obtained from the test results are analysed by the modified size effect law. Subsequently, prediction formulas are proposed, and they are compared with historical test data from the split‐cylinder specimens.     

An experimental study on the tensile strength of steel fiber reinforced concrete

This paper deals with steel fiber reinforced concrete mechanical static behaviour and with its classification with respect to fibers content and mix-design variations. A number of experimental tests were conducted to investigate uniaxial compressive strength and tensile strength. Different mixtures were prepared varying both mix-design and fiber length. Fibers content in volume was of 1% and 2%. Mechanical characterization was performed by means of uniaxial compression tests with the aim of deriving the ultimate compressive strength of fiber concrete. Four-point bending tests on notched specimens were carried out to derive the first crack strength and the ductility indexes. The tensile strength of steel fiber reinforced concrete (SFRC) was obtained both from an experimental procedure and by using an analytical modelling. The experimental tests showed the different behaviour of SFRC with respect of the different fiber content and length. Based on the experimental results, an analytical model, reported in literature and used for the theoretical determination of direct tensile strength, was applied with the aim of making a comparison with experimental results. The comparison showed good overall agreement.     

Effect of strain gradients on the size effect of concrete in uniaxial tension

A series of uniaxial tension experiments has been conducted to investigate the size effect on strength and fracture energy of quasi brittle materials like concrete and sandstone. This paper focuses on the results of the concrete tests, and specifically deals with the variation of the nominal strength for specimens of six different sizes in a scale range of 1:32. It was found that under given experimental conditions, the nominal strength strongly depended on the specimen size. More important however, is the fact that most of this size effect could be attributed to strain gradients which were present in the cross section of the specimens. These strain gradients were caused by the specimen shape, load eccentricity and material inhomogeneity. Through a combination of experimental data and a simple linear elastic analysis, the importance of strain gradients with respect to the ultimate load level could be visualized. This leads to the conclusion that studying a material size effect is not possible without taking into account structural stress/strain gradients. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.     

Effects of geometry and specimen size on out-of-plane tensile strength of aligned CFRP determined by direct tensile method

The out-of-plane tensile strength of CFRP laminate determined by the direct tensile method varies with specimen geometry and size. This effect was first experimentally observed using aligned CFRP. To explain the geometry and size effects from a mechanical point of view, an analytical model combining Weibull statistics, including the concept of effective volume, and a fracture criterion under multi-axial loading was constructed on the basis of stress distributions calculated using the finite element method. The predicted out-of-plane tensile strength of aligned CFRP was found to be consistent with experimental results. Thus, the present model is useful for reducing experimentally determined out-of-plane tensile strength under complex stress distributions to that under a uniaxial and uniform stress distribution.     

虚拟裂缝尖端拉应力大小的确定

针对单边切口的混凝土轴心受拉构件,基于虚拟裂缝模型提出一种计算极限承载力的解析模型,并在此基础上确立了虚拟裂缝尖端拉应力与混凝土轴心抗拉强度之间的关系。结果表明:二者的比值随初始缝高比的增大呈线性增加,但对混凝土强度等级的变化不敏感。其原因是由于所有的混凝土试件都存在初始缺陷,导致截面上存在明显的应力梯度,因而得到的混凝土轴心抗拉强度值是截面应力的平均值,而虚拟裂缝尖端拉应力为截面上的最大应力。很显然,轴心受拉构件的初始缺陷越长,截面的应力梯度越大,虚拟裂缝尖端拉应力与平均应力的比就越大。通常情况下,虚拟裂缝尖端的拉应力大小约为混凝土轴心抗拉强度值的1.22倍,约等于混凝土的抗折强度。     

The nitrogen gas tension test. Part 2: failure mechanism

In this study, the mechanism of concrete failure in the nitrogen gas tension test was investigated through a series of experiments. First, the nitrogen gas tension test was carried out two types of specimens: solid cylinders and hollow cylinders. The test results clearly showed that there was no significant difference in the gas pressure at failure between the solid specimen and the hollow specimen. Since a tension crack occurring on the surface of the concrete specimen at a gas pressure almost equal to the tensile strength of the concrete might play a key role in understanding the failure mechanism, a failure criterion based on linear elastic fracture mechanics (LEFM) was consequently developed. The nitrogen gas tension test was newly carried out on cylindrical specimens with circumferential notches of various depths. Though LEFM was found to be useful in developing an understanding of the mechanism of concrete failure, the experimental results indicated that it was not really valid for specimens with notch depths deeper than some critical size (critical notch depth). However, based on the experimental observation that the concrete specimen failed at its tensile strength at notch depths smaller than the critical notch depth, a modified LEFM based failure mechanism was proposed taking into account the notch sensitivity of the concrete.     

Experimental investigation on uniaxial tensile strength of hybrid fibre concrete

In an experimental study on fracture properties of hybrid fibre concrete, specimens with varying fibre content (mixtures of short and long fibres) were loaded in uniaxial tension. Dog-bone shaped specimens of four different sizes in a size range of 1:8 were tested. Focus of the study was the determination of the size effect on nominal strength and fracture processes. A vacuum impregnation technique was used to investigate the fracture process. Experiments showed that multiple cracks, which formed before the peak, localised into one major crack beyond peak. Multiple cracking could be obtained by increasing the amount of thin short fibres whereas the large fibres can enhance the bridging of localised macrocracks. With decreasing strength, the size effect on the strength appears to increase. It is observed that the size effect on nominal tensile strength decreases with increasing material ductility. Preliminary analysis of the results showed that the observed size effect can be considered as a combination of statistical and structural size effects.     

高强高性能混凝土三轴拉压压力学性能试验研究

采用大型动静真三轴伺服液压试验系统,对单轴压强度为90.6 MPa的高强高性能混凝土进行三轴拉压压等比例试验研究,获得了各应力比下试件的破坏模式、多轴强度及应力-应变曲线。试验结果表明:高强高性能混凝土三轴拉压压应力状态下的破坏为典型的受拉破坏;最大主应力方向的极限强度远低于其单轴压强度,中间主应力效应不明显;拉应力的存在对最大主应力方向应力-应变曲线影响十分明显,呈现出明显的线性特征。基于试验结果提出了适用于高强高性能混凝土的强度准则,为高强高性能混凝土本构关系的建立提供了试验和理论依据。     

Tensile cracking in concrete and sandstone: Part 2—Effect of boundary rotations

This paper contains the second part of our work on tensile cracking that has been conducted over the past years. The behavioural of concrete and sandstone subjected to uniaxial tension is decribed. In part 1 of this paper [1], a numerical lattice model is presented, which is used for explaing fracture mechanisms in heterogenous materials like concrete and sandstone. In the lattice model, the material is schemitzed as a lattice of brittle, breaking beam elements. Cracking is simulated by removing, in each step, the element with the highest stress—to—strength ratio. It was shown that the amount of detail included in the numerical model has a significant effect on the ductility in the load-displacement diagram. In this paper, special attention is given to the effect of varying the rotational stiffiness of the loading platens in uniaxial tensile tests. Experiments are presented of cylindrical specimens of various sizes loaded in tension between non-rotating (fixed) and freely-rotating boundaries. The lattice model is used for a qualitative analysis of the subject. The results suggest that the uniaxial tensile test between freely rotating boudaries yields a (safe?) lower bound for the fracture energy of concrete.     

An experimental method for dynamic tensile testing of concrete by spalling

A new application of the spalling phenomenon in long specimens is reported in this paper. The new experimental technique is based on an experimental setup which consists of an air launcher of cylindrical projectiles with a Hopkinson bar as a measuring tool and a relatively long concrete specimen in contact with the bar. The incident compression wave transmitted by the Hopkinson bar into the specimen is reflected as a tensile wave causing spalling. Although such configurations have been reported in the past, the main advantage of the present approach lies in the application of the detailed analysis, based on the wave mechanics with dispersion, to extract the specimen behaviour. Such an approach leads to an exact estimation of the local failure stress in tension at high strain rates, even above 100 s⁻¹. This paper demonstrates, using two series of tests on concrete, that this experimental setup can cover one decimal order of strain rates, from ∼10 to ∼120 s⁻¹. The tests performed at high strain rates on wet and dry concrete have indicated that the tensile strength is substantially influenced by the loading rate or strain rate. The absolute value of the failure stress for wet and dry concrete is almost the same for a particular strain rate, which does not occur when subject to low strain rates in tension or compression. A brief discussion is offered on a high rate sensitivity of concrete strength in tension at high strain rates.     

Energy dissipation capacity of fibre reinforced concrete under biaxial tension–compression load. Part I: Test equipment and work of fracture

The objective of this research was to analyse the differences in the dissipated energy under uniaxial tension and biaxial tension–compression load of fibre reinforced concretes using the Wedge Splitting Test. Under biaxial load the specimens were subjected to compressive stress ratios from 10% to 50% of the concrete compressive strength perpendicular to the direction of the tensile load.Under biaxial tension–compression load the energy dissipation capacity of the specimens decreases compared to the uniaxial tension load case on average 20–30%. It is believed that the decrease is a result of the damage mechanism of the concrete matrix and deterioration of the fibre–matrix and/or aggregate–cement paste interfaces in case the section is additionally loaded with compression stresses. This indicates that dimensioning of concrete elements under biaxial stress states using material parameters obtained from tests conducted on specimens under uniaxial tensile load is unsafe and could potentially lead to a non-conservative design.In the second part of this paper the extent of the fracture process zone under uniaxial tension and biaxial tension–compression load will be examined with the Acoustic Emission technique and the reasons for decrease of the energy dissipation capacity under biaxial load will be further discussed.     

What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation?

Criteria for predicting initiation of cracks in brittle materials like ceramics are based on two parameters: the material fracture toughness and the tensile strength. Standardized experiments exist to estimate the former. However, the tensile strength is often taken from experiments (mainly uniaxial bending) on specimens with various geometries and surface finish, usually tested under ambient conditions at a given loading rate. The reported strength is commonly the Weibull characteristic strength, which scatters due to the critical defect size distribution on the tested specimen. In this work, we propose a definition of the “inherent” or “intrinsic” tensile strength to be used in numerical models, making a distinction between extrinsic defects due to manufacturing and intrinsic ones relying on the microstructure. Our approach is based on the Finite Fracture Mechanics theory and the Coupled Criterion applied to small surface flaws and its influence on the measured (extrinsic) strength. Numerical results are compared with experiments on alumina reported in the literature. In addition, a model for the Petch law (strength vs. grain size) in polycrystalline materials is proposed using the Coupled Criterion, which predicts an initial crack length of increasing numbers of grains as the grain size decreases.     

骨料粒径对混凝土劈拉性能及尺寸效应影响的细观数值研究

混凝土材料宏观力学行为的非线性及尺寸效应根源于其内部组成的非均质性。考虑材料细观结构非均质性的影响,建立由骨料颗粒、砂浆基质和界面过渡区组成的混凝土细观尺度力学模型。对尺寸为150 mm、250 mm、350 mm和450 mm的混凝土立方体模型劈裂抗拉破坏行为进行细观数值模拟,探讨骨料粒径（最大粒径分别为:10 mm、20 mm、30 mm和40 mm）的影响机制,并与试验结果进行对比分析。结果表明:1） 混凝土材料的劈裂抗拉强度随着骨料粒径增大而略微降低,最大骨料粒径达到30 mm左右时,强度降低趋势变缓;2） 四种骨料粒径下混凝土立方体劈裂抗拉强度均存在尺寸效应现象,相比于大骨料试件,小骨料试件的破坏更具脆性,因而其尺寸效应更显著;3） 混凝土劈裂抗拉强度尺寸效应行为与 Ba?ant和Weibull提出的尺寸效应理论相吻合。     

Effective Tension Active Cross-Section of Reinforced Concrete Beams After Cracking

In the design of concrete structures, estimation of the deflection of the structural members under the service loads is often a critical factor. Strains and displacements are linked to the tension stiffening effect, which is not quantified in the standards. The CEB-FIP model code proposes an interesting simplified method for evaluating the concrete tension stiffening effect on reinforced concrete behavior. One of the parameters which enables the mechanical contribution of the concrete to be quantified is the effective tensile active section of the reinforced concrete beams. In this paper, a new method for calculating the effective tensile active section A _ct.ef is proposed. The calculation is based on an analytical model of stress distribution in the full depth of the concrete section. An experimental study on several reinforced concrete beams is reported. The results show that the new proposed model enhances the accuracy of the beam deflection predictions significantly.     

Application of bridging-law concepts to short-fibre composites Part 3: Bridging law derivation from experimental crack profiles

This is the third paper in a series of four where notch sensitivity, fracture energy and bridging laws are studied in short-fibre polymer composites. Here, bridging laws are derived from experimental crack-opening profiles in centre-hole notched tensile specimens. The materials studied are three types of commercial glass–mat composites with different reinforcement structures and matrices. The materials have softening bridging laws and the calculated fracture energies from bridging laws are in good agreement with values determined directly by experiment. The calculated maximum local bridging stress is found to be higher than the uniaxial tensile strength. An outline of a failure criterion for notched specimens based on the crack-bridging approach is presented.     

Experimental study of size effect on quasi-static strengths for short glass fibre-reinforced plastics

The present paper examines size effect on the strength of short glass fibre-reinforced phenolic resin (SGP) composites made by press moulding with different loading modes and specimen shapes. Three- and four-point flexural tests and tension–torsion combined tests were conducted at room temperature in order to evaluate the influence of V_f and loading mode on fracture strength. The obtained uniaxial strength data were analysed using the Weibull statistical theory. The relationship between fracture strength and effective volume was investigated based on the Weibull statistical theory and agreed well with the effective volume theory (EVT), regardless of specimen size, dimensions or loading mode. The experimental results revealed that the tension–torsion multiaxial SGP strength was in agreement with the Tsai–Hill failure criterion. The EVT was also applied to the Tsai–Hill failure criterion to consider the size effect, and the validity of the proposed method was confirmed experimentally.     

考虑细观组分影响的混凝土宏观力学性能理论预测模型

混凝土宏观力学性能与其内部细观结构构造密切相关。该文建立了一类能够考虑细观组分影响的混凝土宏观力学性能理论预测模型。首先,采用细观力学数值试验法对理论模型中的参数进行了标定;进而,基于该模型对混凝土断裂能和单轴抗拉强度在材料层次的尺寸效应行为进行了分析。结果表明:混凝土断裂能和单轴抗拉强度均随骨料级配（即最大骨料粒径）发生变化,且受到界面特性的影响。当界面过渡区力学性能相对薄弱时,混凝土强度较低,断裂能和单轴抗拉强度随骨料级配增大而呈现减小的趋势;当界面过渡区力学性能较强时,混凝土强度较高,断裂能和单轴抗拉强度随骨料级配增大亦呈现增大的趋势。计算结果与试验结果吻合良好,验证了该文建立的理论预测模型的准确性和合理性。