On the effect of an out-of-plane constraint on the three-dimensional crack front fields in a thin elastic plate

Two-dimensional theories of fracture are still applied widely today and provide theoretical foundations for solutions to many practical problems. These two-dimensional theories are based on the plane strain or plane stress assumption. However, strictly speaking, for a thin elastic plate with a through-thickness crack under tension, plane strain conditions can be met only at the crack front (except the corn point) and plane stress conditions exist at a distance of about one half of the plate thickness from the crack front in the mid-plane. What are the stress fields in the region where both plane strain and plane stress conditions cannot be met? In this paper, further investigations into the problem are carried out. Three-dimensional Maxwell stress functions, the principle of minimum complementary potential energy and three-dimensional J-integrals are employed to obtain an analytical solution to depict the relationship among out-of-plane constraints, three-dimensional J-integrals and stress intensity factors. Three-dimensional finite element simulations with fine meshes are carried out to verify the analytical results. Compared with the corresponding plane strain solution, the solution proposed is valid in a larger region

ENERGY NON-LOCAL MODEL AND NEW STRAIN GRADIENT THEORY

提出一种新的基于能量非局部模型的应变梯度理论,并应用此理论对多晶铜以及薄膜基底的微压痕硬度进行理论预测和数值分析.首先,提出了能量非局部模型,并由此模型,得出新应变梯度理论的本构关系;其次,由变分原理,得出相应的有限元公式;再次,给出了微压痕硬度的有限元分析方法;最后,将该理论预测结果与经典理论预测结果以及实验结果进行了对比.结果表明,计算结果与实验结果相符;而经典理论的预测结果远低于实验结果

能量非局部模型和新的应变梯度理论

提出一种新的基于能量非局部模型的应变梯度理论，并应用此理论对多晶铜以及薄膜基底的微压痕硬度进行理论预测和数值分析．首先，提出了能量非局部模型，并由此模型，得出新应变梯度理论的本构关系；其次，由变分原理，得出相应的有限元公式；再次，给出了微压痕硬度的有限元分析方法；最后，将该理论预测结果与经典理论预测结果以及实验结果进行了对比．结果表明，计算结果与实验结果相符；而经典理论的预测结果远低于实验结果

Three-dimensional fracture analysis for a thin cracked hardening plate

A semi-analytical method is presented to investigate fracture behavior of a mode-I crack in a thin ductile plate. In the part of theoretical analysis, a total deformation theory of plasticity, in conjunction with a power law hardening stress-strain relation, is employed. Three-dimensional Maxwell stress functions, the minimum complementary potential energy principle and three dimensional J-integrals are used to obtain crack front stress fields. In the part of numerical analysis, three dimensional finite element simulations are carried out to obtain J-integrals, the out-of-plane constraint level and crack front stress fields. Comparison with numerical results of crack front stress fields shows the analytic solutions for crack front stress fields are valid. Numerical and analytic results show that the value of the opening stress ahead of the crack front deceases with increasing z (approaching the free surface) and lies between the corresponding plane strain and plane stress solutions

The effect of out-of-plane constraint on the stress fields near the front of a crack in a thin ductile plate

Classical plane solutions based on the elastic-plastic fracture mechanics are applied widely in practical engineering. These plane solutions follow the plane stress or plane strain assumption. However, in the case of a thin ductile plate with a through-thickness crack under tension, plane stress conditions exist at a distance of about one half of the plate thickness ahead of the crack front cross the thickness of the plate. What is the stress state in the region where both plane strain and plane stress conditions cannot be met? In the current paper, a semi-analytical method is presented to investigate the problem. Three dimensional Maxwell stress functions, the minimum complementary potential energy principle and three dimensional J-integrals are employed to obtain solutions for crack front fields in a thin ductile plate. Three-dimensional finite element (FE) analyses are carried out to verify the current solutions. FE results reveal that the out-of-plane constraint level T-z increases with increasing remote loading near the crack front. FE results also show that the in-plane stress fields near the crack front can be characterized by the current J-T-z solutions. Both FE and theoretical results illustrate that opening stresses decrease gradually to the corresponding plane stress HRR-field solutions with increasing radial distance r from the crack front in the mid-plane when remote loading is large enough. (C) 2019 Published by Elsevier Ltd

Strain gradient theory based on a new framework of non-local model

A new framework of non-local model for the strain energy density is proposed in this paper. The global strain energy density of the representative volume element is treated as a non-local variable and can be obtained through a special integral of the local strain energy density. The local strain energy density is assumed to be dependent on both the strain and the rotation-gradient. As a result of the non-local model, a new strain gradient theory is derived directly, in which the first and second strain gradients, as well as the triadic and tetradic stress, are introduced in the context of work conjugate. For power law hardening materials, size effects in thin metallic wire torsion and ultra-thin cantilever beam bend are investigated. It is found that the result predicted by the theoretical model is well consistent with the experimental data for the thin wire torsion. On the other hand, the calculation result for the micro-cantilever beam bend clearly shows the size effect

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level T-z (z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and T-z(z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.</p

New Strain Gradient Theory And Analysis

A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments

用宏基因组学方法研究绿肥对水稻根际微生物磷循环功能基因的影响

【目的】绿肥对土壤微生物磷循环的影响受到研究者们的广泛关注,但绿肥影响土壤磷循环的微生物机理尚不明确。利用宏基因组学方法剖析长期绿肥还田对土壤磷循环功能微生物的影响,旨在阐明绿肥对土壤磷循环影响的微生物机理,为绿肥的科学利用提供依据。【方法】以中国湖南祁阳绿肥及稻草还田定位试验的水稻根际土为材料,利用宏基因组学方法,对土壤微生物DNA进行PE150 (双端读长150 bp)宏基因组测序,使用MetaWRAP软件中的read_qc模块进行质控,用assembly模块megahit方法进行组装;基于组装的较长序列(> 1000 bp)使用Diamond软件的BLASTX和UniProtKB/SWISS-PROT数据库进行序列比对,根据磷活化(磷酸酯矿化、膦酸酯矿化、无机磷溶解)、磷吸收(膦酸酯运输、磷酸酯运输和无机磷酸盐运输)和缺磷诱导响应调控三大类主要磷循环功能相关基因(重点关注的64个磷循环功能基因)进行筛选;再利用R语言进一步分析水稻根际土壤中磷循环功能基因相对丰度及其与土壤理化指标之间的关系,阐述绿肥对土壤磷循环功能微生物的影响。【结果】土壤pH等9个常规指标在有、无绿肥处理之间均无显著差异。无稻草还田时,绿肥处理对64个磷循环功能基因中的11个相对丰度影响显著,这11个基因广泛分布在除磷酸酯运输及无机磷溶解外的5个功能组中,其中phnA、phnN、phnV等3个基因相对丰度上升,phnI、phnL、glpB、glpO、pitA、phoA、phoP、phoU等8个基因相对丰度下降。而在稻草还田时,绿肥处理仅phnPP基因相对丰度显著降低。相关性分析显示,土壤pH与磷酸酶活性、无机磷溶解基因pqqB、pqqC、pqqCD、pqqE、pqqF相对丰度呈显著负相关(P <0.05)。冗余分析(RDA)结果表明,绿肥处理通过pH、AP以及磷酸酶活性影响磷循环功能基因。【结论】绿肥翻压下水稻根际微生物磷功能基因相对丰度深受稻草还田的影响。与单绿肥或单稻草还田相比,绿肥翻压基础上增加稻草还田对磷循环功能基因影响效果不明显,秸秆甚至减弱了绿肥对磷循环功能基因的影响,其原因可能是绿肥和稻草还田下不同微生物及不同磷循环功能基因之间存在激烈竞争