Explicit full-range stress-strain relations for stainless steel at high temperatures

This paper presents a new explicit stress-strain relation for stainless steel at high temperatures. The relation is an approximation of the closed form inversion of an existing two-stage stress-strain relation based on a modified Ramberg-Osgood equation with corresponding temperature-dependent parameters. This new expression for the stress σ, as an explicit function of the total strain ?, is obtained by making a modified power law assumption on the fractional deviation of the actual stress-strain curve from an idealized linear elastic behaviour. The validity of the inverted expression is tested over a wide range of material parameters and a wide range of temperatures. The tests show that the new expression results in stress-strain curves which are both qualitatively and quantitatively consistent with the fully iterated numerical solution of the full-range stress-strain relation for normal as well as high temperatures.     

拉压下不锈钢三阶段应力-应变关系的逆表达式

提出了不锈钢合金应力-应变关系的新表达式,应力为应变的显式函数。基于改进的Ram-berg-Osgood方程,本公式是现有三阶段应力-应变关系的一种近似逆表达。三阶段关系公式比两阶段关系公式更准确,并对拉应力和压应力均适用。基于理想线弹性性能和实际应力-应变曲线误差的合理假定,提出本表达式,其在应力的全范围阶段都是有效的。选取不同的材料参数,对本表达式进行试验验证。结果表明:新公式结果与全范围应力-应变关系的迭代数值求解结果很吻合,最大误差低于4%。     

A three-stage full-range stress–strain inversion for stainless steel alloys as an explicit function of temperature

Presented in this paper is a new explicit full-range stress–strain inversion for stainless steel alloys which expresses the stress as an explicit function of strain and temperature. The relation utilizes an approximation of the closed form inversion of a highly accurate three-stage stress–strain relation recently obtained from a modified version of the Ramberg–Osgood equation. The inversion which is obtained by making a generalized rational function assumption on the fractional deviation of the actual stress–strain curve from an idealized linear elastic behavior is applicable both to tensile and compressive stresses. The temperature dependence is then accounted for by using modified mechanical properties which are functions of temperature. The paper also presents a new direct temperature dependent stress–strain relation based on material properties at normal temperature. While previous studies use temperature dependent material properties to account for the effect of temperature on the stress–strain relation, this paper proposes explicit formulation based on the material properties at normal temperatures. The explicit temperature dependence is introduced by modifying the form of the stress–strain relation which includes a factor with an appropriate temperature dependent function. The validity of the temperature-dependent expression is tested over a wide range of material parameters and a wide range of temperatures. It is demonstrated that the proposed expression is both qualitatively and quantitatively in excellent agreement with the fully iterated numerical solution of the full-range temperature-dependent stress–strain relation at moderate and high temperatures.     

An explicit stress formulation for stainless steel applicable in tension and compression

In this paper an explicit stress formulation for stainless steel is presented. The formulation is applied to both tension and compression and it is an approximation to the closed form inversion of an existing two-stage stress-strain relation which is based on a modified Ramberg-Osgood equation. The validity of the explicit expression is tested over a wide range of material parameters. The tests demonstrate that the explicit formula is in excellent agreement with the fully iterated numerical solution of the full-range stress-strain relation. By incorporating an existing expression for deformation capacity, the proposed explicit formula is also used to obtain an explicit formulation for the computation of local buckling stress and compression resistance in terms of cross sectional slenderness.     

考虑吸附作用的含气煤本构关系

 利用混合物理论本构建模的方法,给出含气煤饱和混合物的本构方程,方程中混合物组分体积分数反映煤体内部结构的变化,并建立组分应力与真实应力之间的联系。考虑含气煤为各向同性弹性体,根据弹性能与表面能的变化相等条件下吸附作用引起的煤体体积变形,得出含气煤饱和混合物中各组分体积分数,进而由本构方程推导三轴应力条件下含气煤的应力–应变关系。通过考察不同吸附性气体的煤样应力–应变曲线,分析吸附作用对含气煤本构关系的影响,并将试验曲线与理论预测进行比较。研究结果表明,含气煤试验曲线与理论值吻合良好,理论公式可用于描述与气体吸附性有关的煤体变形差异。即使煤的骨架结构满足虎克弹性体本构关系假定,在孔隙率和孔隙压力相同条件下,气体吸附性的差异仍将改变含气煤的应力–应变关系。     

Small Strain Stiffness and Non-Linear Stress-Strain Behaviour of Cement-Mixed Gravelly Soil

The stiffness at small strains and non-linear stress-strain relation of compacted cement-mixed well-graded gravelly soil as well as the ageing effects were evaluated by drained triaxial compression tests on compacted moist specimens cured for different periods at isotropic and different anisotropic stress states. In all the tests, the initial stress-strain relation at small strains less than about 0.001% was essentially elastic and the initial Young's modulus, E₀, was essentially the same as the E_eq value evaluated by applying unload/reload cycles under otherwise the same conditions. The E_eq values were rather independent of strain rate. The E_eq value from the first unload/reload cycle applied during otherwise continuous ML became noticeably lower than the elastic modulus evaluated at the same stress state, more as approaching the peak stress state. After a number of small unload/reload cycles and long sustained loading, the E_eq value became closer to the elastic modulus due to a decrease in the viscous effects. The ratio of E₀ to the compressive strength (q_max) was similar to that of concrete but noticeably larger than those of uncompacted cement-mixed soil, sedimentary softrock and unbound gravelly soil. Both E₀ and q_max increased with time by ageing, while the E₀/q_max ratio decreased with time. When ML was restarted at a constant strain rate after ageing with a shear stress, the tangent stiffness became very high for a large stress range with a substantial change in the non-linearity of stress-strain relation.     

建筑垃圾细料生产流动化回填材料的性能

以灰砂比0.03、0.05和0.08,粉砂比0、0.05、0.1、0.15和0.2为设计参数,对建筑垃圾回填材料进行设计。通过试验对回填材料的流动性(流动度、泌水率)、无侧限抗压强度以及应力应变曲线、本构关系模型和弹性模量等进行研究。研究结果表明:回填材料的流动度受水固比影响较大,两者接近线性关系;流动度在200~250mm范围,泌水率在4%~8%之间;回填材料抗压强度与灰砂比和水固比之间存在很好的幂指数关系;回填材料应力应变曲线形状与普通混凝土的相似,在此基础上提出回填材料的本构关系模型;回填材料无侧限抗压强度与弹性模量之间存在很好的指数关系。     

Local buckling of thin-walled pipes being bent in the plastic range

The well-known ‘strut on an elastic foundation’ theory for studying elastic buckling of axial loaded thin cylinders is reworked so that it can be used to study buckling of pipes during cold field bending. This operation involves straining of the material well into the plastic range so any buckling will be post-elastic. In order to use the theory, the moduli in the circumferential and longitudinal directions have to be selected and the considerable experimental evidence from pipes of widely differing geometry and materials support the choice as Young's modulus, E, for the modulus in the circumferential direction and the tangent modulus in the longitudinal direction. A simple graphical method enables both the stress and strain at buckling and the peak-to-peak distance between buckles to be predicted. The paper concludes with observations about the important influence that the shape of the stress-strain curve has upon buckling behaviour.     

基于Lade-Duncan和SMP两种强度准则的岩石残余应力研究

 首先利用平面强度理论推导出基于Lade-Duncan和SMP两种准则的强度统一表达式,并结合岩石材料峰后应变软化的力学特性,以峰后内摩擦角?为中间变量,用残余应变 ? 来表示峰后非线性弹性模量E,最后建立岩石峰后残余应力的统一非线性本构方程(即峰后本构模型)。结合小官庄铁矿东区典型破裂岩闪长玢石的三轴试验,对该试验结果进行不同围岩下峰后应力–应变关系的模拟计算。结果表明,建立的峰后本构关系能较好地模拟试验结果,从而验证该模型的合理性,为研究岩石峰后力学规律提供新的途径。     

邓肯E-B模型弹性部分能量守恒的探讨

 邓肯E-B模型的卸荷再加荷模量和体积模量出发,以热力学定律为基础,构造土体的吉布斯自由能函数,通过勒让德变换,得到增量的应力–应变关系。采用热力学方法对柔度矩阵进行修正,从而产生弹性体应力(或应变)与弹性剪切应变(或应力)的耦合项。经典的弹性本构认为剪切与胀缩效应是不相关的,但几个闭合应力路径的计算表明,其能量存在不守恒问题。所提出的修正模型能够满足闭合应力路径的能量守恒,且能更好地拟合三轴试验弹性应力–应变关系。     

混凝土多孔砖砌体单轴受压应力应变特征点试验研究

通过逆向加载的方式对混凝土多孔砖砌体的应力-应变曲线进行试验.分析了混凝土多孔砖强度、砂浆强度对砌体的应力-应变曲线各特征点应力、应变的影响.结果表明,混凝土多孔砖强度对峰值应力的影响高于砂浆强度;弹性阶段的变形主要是受压时砂浆的变形;残余变形阶段破碎砌体间的胶合和摩擦力主要依靠的是砂浆.     

岩石非线性弹性的实验研究及其P-M模型的理论解释

岩石介质由于自身的不均匀性如微孔隙和微裂纹的普遍存在，可以认为是非线性弹性介质，它的重要特征之一就是应力．应变曲线的滞回现象。对不同的岩石样品在MTS伺服压力机上进行了一系列的循环加、卸载实验，得到了不同岩石的应力．应变的滞回曲线。Preisach-Mayergoyz模型(简称P-M模型)是一种从微观概率分布入手研究滞回现象的理论。在简要阐述了该模型的基本原理后，研究了微观模型参数变化对宏观力学性质(如应力．应变曲线和动静态弹性模量等)的影响，结合一组实验数据推算出岩石样品的模型参数，利用这些参数得出其他组的理论曲线，发现理论曲线与实验得到的应力-应变曲线、弹性模量曲线基本吻合。这证明P-M模型在模拟岩石中的微孔隙和微裂纹在低应力状态下对岩石力学性质的影响时是一种有效的方法。最后，对模型的适用范围和改进办法进行了讨论。     

Stress-Strain Relationship of Frozen Sand as a Composite Geomaterial

The present paper aims at developing a simplified model for a stress-strain relationship at small strains up to an initial yielding of homogeneous saturated frozen sand. The modelling of elastic moduli for an ice-sand mixture as a composite geomaterial is first introduced based on previous studies, where a saturated frozen sand is treated as the ice- sand mixture. The applicability of modelling the elastic moduli under constant temperature is then discussed from the theoretical and experimental points of view. In addition, the hyperbolic stress-strain modelling of saturated frozen sand at small strain is presented. The effect of the volume fraction of sand, stiffness of sand inclusion and temperature changes on the elastic moduli and the stress-strain behaviour up to about 1-2% axial strain, which is defined as an upper yield stress, are investigated through the model, whose applicability is verified in comparison with the experimental data.     

考虑主应力轴旋转效应的交通荷载下饱和软黏土变形特性试验研究

 采用空心圆柱扭剪仪对原状饱和软黏土开展交通荷载诱发主应力幅值与主应力轴旋转耦合加载路径下的不排水试验研究。通过与循环三轴压缩试验对比,探讨主应力轴旋转对孔压、变形和应力–应变的影响。分析广义剪应力对循环刚度和非共轴性的影响。试验结果表明,相比较循环三轴试验,交通荷载应力路径下所诱发的主应力轴旋转使孔压和应变显著变大,应力–应变滞回圈刚度显著弱化。循环耦合加载路径下,存在剪切应力–应变和正偏应力–应变2种响应,应力–应变刚度呈现各向异性弱(强)化,应变增量矢量有显著的非共轴性,非共轴性有显著分段特征。较低剪应力水平下,应变路径轨迹趋于稳定,循环刚度表现为强化,非共轴性趋于增大;而较高剪应力水平下,应变路径轨迹趋于破坏,随循环弱化,非共轴性减小。     

工程中典型应力路径下土的应力-应变特性分析

分别采用Mohr-Coulomb模型、修正剑桥模型和UH模型预测正常固结土在常规三轴压缩、三轴伸长和平均主应力p减小的压缩工况中典型路径下土的变形特性。Mohr-Coulomb模型为理想弹-塑性模型,屈服之前为弹性变形,屈服之后为变形无限增大的弹-塑性变形。修正剑桥模型能够较好地模拟压缩路径条件下正常固结土的应力-应变...     

双向应力作用下钢筋混凝土板非线性本构关系

以复杂几何形状、边界条件及配筋形式的钢筋混凝土薄板为研究对象,根据钢筋混凝土有限元理论,以三角形分层组合式的弹性薄板弯曲单元为基础,研究了混凝土为各向异性材料在双向应力作用下的本构关系。     

岩石三维破裂过程的数值模拟研究

采用细观弹性损伤模型和有限元计算方法实现岩石三维破裂过程的数值模拟。考虑到岩石非均匀性的本质特征，通过引入简单直观的单元本构模型，采用细观单元材料性质退化的办法，利用位移加载来实现岩石逐渐破裂过干旱；模拟单轴压缩、单轴拉伸和剪切破裂3种基本试验，得到岩石非线性应力-应变曲线和不同载荷阶段三维损伤破裂演化系列图像；分析细观非均匀性对岩石宏观破裂力学行为的影响。试验研究表明，三维破裂比二维破裂更为复杂，RFPA^3D可以有效地模拟脆性材料的三维破裂。     

纯主应力轴旋转下饱和软黏土的循环弱化及非共轴性

采用空心圆柱扭剪仪对原状饱和软黏土进行了纯主应力轴旋转应力路径的循环不排水试验,加载过程中维持平均应力、广义剪应力和中主应力系数不变。观测了孔隙水压和各应变分量在循环加载过程中的变化特性,着重探讨了中主应力系数及广义剪应力对变形刚度以及非共轴特性的影响规律。主应力偏转的循环剪切路径下,存在扭转剪切和轴向剪切两种不同的循环应力应变响应。试验结果表明:循环加载路径下饱和软黏土的孔压及应变产生累积效应,应力应变刚度呈现各向异性弱(强)化效应,而应变增量呈现显著的非共轴性;中主应力系数b影响特性表现为,b值越大则刚度弱化越显著。试验观察还发现,剪应力水平较低时循环变形刚度表现为强化,非共轴角趋于增大;反之,剪应力水平较高时,伴随着循环弱化,非共轴角趋于减小。     

青藏高原黄土区护坡灌木植物根系力学 特性研究

 为研究灌木根系固土护坡的力学机制,以西宁盆地为例,对青藏高原黄土区柠条锦鸡儿、白刺、霸王、四翅滨藜4种灌木进行室内单根拉伸、剪切试验,系统分析灌木根系材料的力学特性。试验与研究结果表明：根系抗拉力和抗剪力均与根径呈幂函数或指数函数关系,且随根径增大而增大,生长期为18个月的4种灌木的抗拉力与抗剪力大小依次为：四翅滨藜＞柠条锦鸡儿＞霸王＞白刺;根系抗拉强度与根径间呈幂函数或指数函数的关系,随根径增大而减小。根系拉伸的应力–应变特征随不同灌木种的根系结构组成不同而不同,4种灌木种单根拉伸应力–应变曲线均表现出在根系受拉后的初期阶段,应力–应变呈直线关系,当荷载超过弹性极限,拉力继续增加时,应力–应变关系反映出非线性弹性特征,4种灌木种延伸率均可达13%以上,且根系最大延伸率随根径增大而降低。研究区根系密集且毛细根分布较多的0.3～0.8 m的浅层土体具有较大的抗拉强度、抗剪强度和抗变形能力,对防治边坡表层水土流失、增强根–土复合体抗剪强度、减缓与防治边坡的滑移变形具有重要作用。根据4种供试灌木根系力学特性并结合根系形态特征,四翅滨藜和柠条锦鸡儿根系固土护坡作用较大。     

Estimation of the Small-Strain Stiffness of Clean and Silty Sands using Stress-Strain Curves and CPT Cone Resistance

The initial, linear elastic range of a soil stress-strain curve is often defined by the small-strain elastic modulus E₀ or shear modulus G₀. In the present study, simpler and effective methods are proposed for the estimation of the small-strain stiffness of clean and silty sands; these are based on triaxial compression test results and the CPT cone resistance q_c. In the method based on stress-strain curves obtained from triaxial compression tests, an extrapolation technique is adopted within the small-strain range of a transformed stress-strain curve to obtain estimates of the small-strain elastic modulus. Calculated small-strain elastic modulus values were compared with the values measured using bender element tests performed on clean sands and sands containing nonplastic fines. The results showed that the method proposed produces satisfactory estimates of the small-strain elastic modulus for practical purposes. In the CPT-based method, two G₀-q_c correlations available in the literature were evaluated. For isotropic conditions, both correlations produced reasonably good estimates of G₀ for clean sands but overestimated it for silty sands. A G₀-q_c correlation which is proposed takes into account the effect of silt content of the sand and stress anisotropy.