基于损伤断裂理论的混凝土破坏行为研究
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摘要
混凝土是由粗骨料、细骨料和水泥浆组成的非均质混合物,但其表现出来的力学性能并不是这几种材料性能的简单叠加,而是与其内部的组成结构紧密相关。混凝土具有微观、细观、宏观等不同的层次结构,在成型过程中又不可避免的存在着气泡、夹杂、微裂缝等初始缺陷,这些因素使得混凝土的力学性能极为复杂。以往对于混凝土的研究大多基于宏观层次,将混凝土看作是单一匀质的材料,这种均匀化的处理方法对于研究混凝土结构的宏观力学性能无疑是行之有效的,但是要想深入研究混凝土的工作机理还应从混凝土的细观组成结构入手,抓住材料非均质性的特点,揭示混凝土结构宏观表现的内在机制。本文首先在细观层次建立了混凝土的数值模型,分析了混凝土损伤破坏机理,以此为基础在宏观层次提出了混凝土损伤断裂理论分析模型,通过宏、细观两个层次的相互联系与补充对混凝的破坏行为进行研究。
在细观层次将混凝土看作是由粗骨料、硬化水泥砂浆和界面组成的三相复合材料,建立了混凝土三维细观数值模型。该模型以球体表示粗骨料的形状,采用蒙特卡洛法结合占位剔除算法实现骨料的随机投放。采用概率分布与随机赋值的方法对各细观相单元材料力学参数进行赋值,实现了对混凝土材料非均匀性的模拟。根据细观相材料损伤演化特点,模型采用带残余强度的各向同性弹性损伤本构方程和最大拉应变破坏准则。建立了6组混凝土立方体试件数值模型,对影响细观数值模型的参数进行分析。结果表明,骨料的不同随机分布形式对局部区域损伤破坏路径和分布有影响,对试件承载力和整体损伤程度的影响可以忽略。界面的弹性模量对混凝土的承载力影响要比砂浆的影响显著。当考虑细观相材料的非均匀性时,混凝土的承载力低于不考虑非均匀性时的承载力。界面和砂浆损伤本构模型中的残余应变系数对试件混凝土损伤发展速度和承载力都有较为明显的影响,当细观相材料的残余应变系数增加时,该相单元损伤速度减慢,混凝土承载力有所提高。依据混凝土细观模型建立方法和影响参数的分析结果,对混凝土梁和棱柱体轴心受拉试件采用位移加载方式,进行了加载至破坏全过程的数值模拟,捕捉了受拉区裂缝的产生、演化及汇聚过程,显示了混凝土准脆性破坏的特点。
在混凝土细观数值模型的基础上,通过引入钢筋和钢筋—砂浆界面单元,建立了钢筋混凝土细观数值模型。分别对月牙肋钢筋和螺纹钢筋单端拉拔试件进行了细观数值模拟,分析了钢筋肋外形对混凝土损伤的影响。月牙肋和螺纹肋钢筋试件总体破坏形态较为相似,在钢筋拉拔过程中,加载端受到拉拔力的挤压作用较大,且钢筋周围混凝土应力较高,远离钢筋处混凝土应力较低,混凝土损伤呈现了从钢筋外周向试件四边逐渐衰减的趋势。损伤和破坏首先发生在加载端的钢筋—砂浆界面上,并沿界面逐渐向自由端发展。随着拉拔力的增加,破坏的钢筋—砂浆界面单元和砂浆单元逐渐贯通,宏观上表现为钢筋肋间混凝土咬合齿依次发生破坏,形成纵向滑移裂缝。月牙肋钢筋拉拔试件的损伤单元呈现锥形分布,钢筋周围混凝土的应力集中较为缓和,螺纹钢筋拉拔试件的损伤单元则呈现梭形分布,应力集中明显,混凝土损伤程度较重。
在宏观层次,根据混凝土裂缝前端断裂过程区的特点,假设混凝土断裂过程区由微裂缝生成区和微裂缝扩展区两部分组成。将损伤力学和断裂力学理论相结合,提出了混凝土D-K损伤断裂模型,该模型以起裂损伤阈值DIG作为混凝土的起裂判据,以失稳断裂韧度KIC作为裂缝失稳扩展判据,实现了从初始损伤到宏观裂缝形成直至裂缝失稳扩展破坏整个过程的分析。由于采用损伤起裂判据,从而克服了现有混凝土断裂模型无法分析没有初始宏观裂缝的混凝土起裂的局限性,且模型判据具有明确的物理意义。根据Ⅰ型裂纹尖端弹性应力场分布,推导了不同屈服准则下微裂缝生成区形态的表达式,对比了微裂缝生成区的轮廓,对混凝土拉压强度比a、泊松比v和中间主应力等参数的影响进行了分析。基于细观数值模拟和相关文献试验得到的轴心受拉试件的软化曲线提出了分段幂函数损伤模型,并据此确定了等效裂缝上闭合力的分布规律,推导了混凝土起裂损伤阈值DIG的表达式及断裂过程区的最大长度。采用数值方法分别对有、无初始裂缝的混凝土三点弯曲梁的裂缝开展进行了数值模拟,验证了D-K模型数值求解的可行性和有效性,分析了初始缝高比对失稳断裂韧度KIC的影响。
从混凝土的细观多相结构到宏观单一材料是均匀化的过程,通过均匀化能够反映混凝土细观组成与宏观性质之间的定量关系。基于复合材料细观夹杂理论,建立了计算混凝土弹性模量的混合夹杂模型,利用广义自洽方法和Mori-Tanaka方法推导了模型的解析解,并对骨料体积百分比、界面厚度及其弹性模量,孔洞和微裂缝的含量等主要影响因素进行了分析。
Concrete is a heterogeneous mixture of coarse aggregate, fine aggregate and cement slurry, its mechanical properties is closely related to its internal composition structure rather than simple superposition of composing materials'mechanical properties. Concrete has different structure forms at micro-level, meso-level and macro-level. Meanwhile, initial imperfections such as bubbles, inclusions and micro-cracks inevitably produced during molding process. All the factors above make the mechanical properties of concrete become extremely complex. The previous researches on concrete are mostly based on macro-level, and take concrete as a single homogeneous material. Without a doubt, the homogenization approach is effective in the research of concrete's macroscopic mechanical properties. However, in order to reveal the internal mechanism of concrete's macroeconomic performance, and study its working mechanism deeply, researchers should start with the microscopic composition of concrete, and seize the heterogeneity characteristics of concrete material. In this paper, numerical model of the concrete at meso-level was established at first, the damage and failure mechanism was then analyzed. Based on these, analysis model of damage and fracture theory was proposed at macro-level. The fracture behavior of concrete was researched between meso-level and macro-level with the relationship and complement of them.
Concrete was considered as a three-phase composite material composing of aggregates, mortar and bonding material at meso-level. A3-D mesoscopic numerical model with random aggregate and mechanical parameter was proposed. This model can simulate the random distribution of aggregates. Furthermore, according to a random distribution, the mechanical parameters of the meso-phase elements in this model can be assigned. Thus the nonhomogeneiry simulation of concrete has realized. Six groups of concrete cube numerical model were established, the parameters which influence mesoscopic numerical model have been analyzed. The results show that the random distributing of aggregate location has influence on the generating location and expanding paths of crack, while its influence on the carrying capacity of specimens can be neglected. The elastic modulus of interface has greater influence on carrying capacity of concrete than that of mortar. The carrying capacity of concrete descends when taking the non-uniformity of the meso-phase materials into account. The residual strain coefficient in damage constitutive model of interface and mortar has a significant effect on the development speed of damage and the carrying capacity of the specimens. If the residual strain coefficient of a certain meso-phase material increases, the damage speed of elements with this phase will reduces, and the carrying capacity of concrete will increases slightly. According to the above model and analysis results, utilizing the method of displacement loading, the loads were imposed on the concrete beam and the prism axis tensile specimen gradually untill they became damaged, and the status of the beam and specimen all through the process were simulated numerically. The process of crack appearance and growth were obtained and the quasi-brittle failure characteristic of concrete was also revealed.
Based on the mesoscopic model for concrete, steel bars and bar-mortar interface were used to establish a reinforced concrete numerical model. Pullout test of crescent-ribbed bar specimens and screw thread bar specimens were simulated respectively, the influence of rib outline on concrete damage was analyzed. Results show that the overall failure patterns of these two specimens are similar to each other. During the pullout process, stronger squeezing action appears at the load-end, moreover, the stress of concrete around steel bar is stronger than that away from it. The damage of concrete presents a gradually decay trend from the circumambience of steel bar to specimen outsides. Damage and failure occurs first in the steel bar-mortar interface of the load-end and extends gradually to the free end. With the increase of the pulling force, the failure elements of steel bar-mortar interface and mortar gradually impenetrate, the occlusion gears of concrete among steel bar ribs destruct in turn, and the longitudinal sliding cracks come into being. The damage elements of crescent-ribbed bar specimen distribute a taper pattern, the stress concentration in concrete around steel bar is low. As a contrast, the damage elements of screw thread bar specimen distribute a shuttle pattern, the stress of concrete is obviously concentrated, and the damage of concrete is more severe.
At the macro level, the concrete fracture process zone was assumed to be consist of micro-crack generating zone and developing zone according to its characteristics. Combining the damage theory and fracture mechanics, a damage-fracture model named D-K model for concrete was put forward. This model takes the initial fracture damage threshold, DIG as the incipient cracking criterion and unstable fracture toughness, KIc as the crack unstable growth criterion. Based on this method, the whole damage and fracture process from initial damage, macro-crack forming to crack unstably propagating can be analyzed. It is known that the shortcoming of existing fracture models is they cannot analyze specimens without original cracks. However, in this model, the damage incipient cracking criterion is innovative used, which not only has the definite physical meaning but also can overcome the shortcoming above. Furthermore, according to the elastic stress field distribution of type I crack tip, several micro-crack generating zone outline expression has been derived under different yield criteria. The influence of concrete tension and compression strength ratio, Poisson's ratio and the intermediate principal stress on outline was analyzed. Based on the softening curve of pullout specimens from mesoscopic numerical simulation and physical tests, the author tried to propose a segmental power function damage model and determine the distribution rule of cohesive stress of equivalent crack according to the model. The expressions of concrete initial fracture damage threshold, as well as the ultimate length of the fracture process zone were derived. The crack growth process of three-point bending concrete beams with and without original cracks was simulated using numerical methods. And then the feasibility and validity of numerical solving method with D-K model were verified. Finally, the influence of initial ao/D on unstable fracture toughness, KIc was discussed.
It is a homogenization process for concrete from meso multiphase structure to macroscopic uniform material, the quantitative relationship between the meso composition and macroscopic properties can be reflected by homogenization. Based on inclusion theory of composite materials, a mixture inclusion model for concrete was put forward, the analytical solution for the model was derived with generalized self-consistent and Mori-Tanaka method. The elastic modulus of concrete was predicted using this model, the main influencing factor such as aggregate volume percentage, interface thickness, elastic modulus, content of void and micro cracks were analyzed.
在细观层次将混凝土看作是由粗骨料、硬化水泥砂浆和界面组成的三相复合材料,建立了混凝土三维细观数值模型。该模型以球体表示粗骨料的形状,采用蒙特卡洛法结合占位剔除算法实现骨料的随机投放。采用概率分布与随机赋值的方法对各细观相单元材料力学参数进行赋值,实现了对混凝土材料非均匀性的模拟。根据细观相材料损伤演化特点,模型采用带残余强度的各向同性弹性损伤本构方程和最大拉应变破坏准则。建立了6组混凝土立方体试件数值模型,对影响细观数值模型的参数进行分析。结果表明,骨料的不同随机分布形式对局部区域损伤破坏路径和分布有影响,对试件承载力和整体损伤程度的影响可以忽略。界面的弹性模量对混凝土的承载力影响要比砂浆的影响显著。当考虑细观相材料的非均匀性时,混凝土的承载力低于不考虑非均匀性时的承载力。界面和砂浆损伤本构模型中的残余应变系数对试件混凝土损伤发展速度和承载力都有较为明显的影响,当细观相材料的残余应变系数增加时,该相单元损伤速度减慢,混凝土承载力有所提高。依据混凝土细观模型建立方法和影响参数的分析结果,对混凝土梁和棱柱体轴心受拉试件采用位移加载方式,进行了加载至破坏全过程的数值模拟,捕捉了受拉区裂缝的产生、演化及汇聚过程,显示了混凝土准脆性破坏的特点。
在混凝土细观数值模型的基础上,通过引入钢筋和钢筋—砂浆界面单元,建立了钢筋混凝土细观数值模型。分别对月牙肋钢筋和螺纹钢筋单端拉拔试件进行了细观数值模拟,分析了钢筋肋外形对混凝土损伤的影响。月牙肋和螺纹肋钢筋试件总体破坏形态较为相似,在钢筋拉拔过程中,加载端受到拉拔力的挤压作用较大,且钢筋周围混凝土应力较高,远离钢筋处混凝土应力较低,混凝土损伤呈现了从钢筋外周向试件四边逐渐衰减的趋势。损伤和破坏首先发生在加载端的钢筋—砂浆界面上,并沿界面逐渐向自由端发展。随着拉拔力的增加,破坏的钢筋—砂浆界面单元和砂浆单元逐渐贯通,宏观上表现为钢筋肋间混凝土咬合齿依次发生破坏,形成纵向滑移裂缝。月牙肋钢筋拉拔试件的损伤单元呈现锥形分布,钢筋周围混凝土的应力集中较为缓和,螺纹钢筋拉拔试件的损伤单元则呈现梭形分布,应力集中明显,混凝土损伤程度较重。
在宏观层次,根据混凝土裂缝前端断裂过程区的特点,假设混凝土断裂过程区由微裂缝生成区和微裂缝扩展区两部分组成。将损伤力学和断裂力学理论相结合,提出了混凝土D-K损伤断裂模型,该模型以起裂损伤阈值DIG作为混凝土的起裂判据,以失稳断裂韧度KIC作为裂缝失稳扩展判据,实现了从初始损伤到宏观裂缝形成直至裂缝失稳扩展破坏整个过程的分析。由于采用损伤起裂判据,从而克服了现有混凝土断裂模型无法分析没有初始宏观裂缝的混凝土起裂的局限性,且模型判据具有明确的物理意义。根据Ⅰ型裂纹尖端弹性应力场分布,推导了不同屈服准则下微裂缝生成区形态的表达式,对比了微裂缝生成区的轮廓,对混凝土拉压强度比a、泊松比v和中间主应力等参数的影响进行了分析。基于细观数值模拟和相关文献试验得到的轴心受拉试件的软化曲线提出了分段幂函数损伤模型,并据此确定了等效裂缝上闭合力的分布规律,推导了混凝土起裂损伤阈值DIG的表达式及断裂过程区的最大长度。采用数值方法分别对有、无初始裂缝的混凝土三点弯曲梁的裂缝开展进行了数值模拟,验证了D-K模型数值求解的可行性和有效性,分析了初始缝高比对失稳断裂韧度KIC的影响。
从混凝土的细观多相结构到宏观单一材料是均匀化的过程,通过均匀化能够反映混凝土细观组成与宏观性质之间的定量关系。基于复合材料细观夹杂理论,建立了计算混凝土弹性模量的混合夹杂模型,利用广义自洽方法和Mori-Tanaka方法推导了模型的解析解,并对骨料体积百分比、界面厚度及其弹性模量,孔洞和微裂缝的含量等主要影响因素进行了分析。
Concrete is a heterogeneous mixture of coarse aggregate, fine aggregate and cement slurry, its mechanical properties is closely related to its internal composition structure rather than simple superposition of composing materials'mechanical properties. Concrete has different structure forms at micro-level, meso-level and macro-level. Meanwhile, initial imperfections such as bubbles, inclusions and micro-cracks inevitably produced during molding process. All the factors above make the mechanical properties of concrete become extremely complex. The previous researches on concrete are mostly based on macro-level, and take concrete as a single homogeneous material. Without a doubt, the homogenization approach is effective in the research of concrete's macroscopic mechanical properties. However, in order to reveal the internal mechanism of concrete's macroeconomic performance, and study its working mechanism deeply, researchers should start with the microscopic composition of concrete, and seize the heterogeneity characteristics of concrete material. In this paper, numerical model of the concrete at meso-level was established at first, the damage and failure mechanism was then analyzed. Based on these, analysis model of damage and fracture theory was proposed at macro-level. The fracture behavior of concrete was researched between meso-level and macro-level with the relationship and complement of them.
Concrete was considered as a three-phase composite material composing of aggregates, mortar and bonding material at meso-level. A3-D mesoscopic numerical model with random aggregate and mechanical parameter was proposed. This model can simulate the random distribution of aggregates. Furthermore, according to a random distribution, the mechanical parameters of the meso-phase elements in this model can be assigned. Thus the nonhomogeneiry simulation of concrete has realized. Six groups of concrete cube numerical model were established, the parameters which influence mesoscopic numerical model have been analyzed. The results show that the random distributing of aggregate location has influence on the generating location and expanding paths of crack, while its influence on the carrying capacity of specimens can be neglected. The elastic modulus of interface has greater influence on carrying capacity of concrete than that of mortar. The carrying capacity of concrete descends when taking the non-uniformity of the meso-phase materials into account. The residual strain coefficient in damage constitutive model of interface and mortar has a significant effect on the development speed of damage and the carrying capacity of the specimens. If the residual strain coefficient of a certain meso-phase material increases, the damage speed of elements with this phase will reduces, and the carrying capacity of concrete will increases slightly. According to the above model and analysis results, utilizing the method of displacement loading, the loads were imposed on the concrete beam and the prism axis tensile specimen gradually untill they became damaged, and the status of the beam and specimen all through the process were simulated numerically. The process of crack appearance and growth were obtained and the quasi-brittle failure characteristic of concrete was also revealed.
Based on the mesoscopic model for concrete, steel bars and bar-mortar interface were used to establish a reinforced concrete numerical model. Pullout test of crescent-ribbed bar specimens and screw thread bar specimens were simulated respectively, the influence of rib outline on concrete damage was analyzed. Results show that the overall failure patterns of these two specimens are similar to each other. During the pullout process, stronger squeezing action appears at the load-end, moreover, the stress of concrete around steel bar is stronger than that away from it. The damage of concrete presents a gradually decay trend from the circumambience of steel bar to specimen outsides. Damage and failure occurs first in the steel bar-mortar interface of the load-end and extends gradually to the free end. With the increase of the pulling force, the failure elements of steel bar-mortar interface and mortar gradually impenetrate, the occlusion gears of concrete among steel bar ribs destruct in turn, and the longitudinal sliding cracks come into being. The damage elements of crescent-ribbed bar specimen distribute a taper pattern, the stress concentration in concrete around steel bar is low. As a contrast, the damage elements of screw thread bar specimen distribute a shuttle pattern, the stress of concrete is obviously concentrated, and the damage of concrete is more severe.
At the macro level, the concrete fracture process zone was assumed to be consist of micro-crack generating zone and developing zone according to its characteristics. Combining the damage theory and fracture mechanics, a damage-fracture model named D-K model for concrete was put forward. This model takes the initial fracture damage threshold, DIG as the incipient cracking criterion and unstable fracture toughness, KIc as the crack unstable growth criterion. Based on this method, the whole damage and fracture process from initial damage, macro-crack forming to crack unstably propagating can be analyzed. It is known that the shortcoming of existing fracture models is they cannot analyze specimens without original cracks. However, in this model, the damage incipient cracking criterion is innovative used, which not only has the definite physical meaning but also can overcome the shortcoming above. Furthermore, according to the elastic stress field distribution of type I crack tip, several micro-crack generating zone outline expression has been derived under different yield criteria. The influence of concrete tension and compression strength ratio, Poisson's ratio and the intermediate principal stress on outline was analyzed. Based on the softening curve of pullout specimens from mesoscopic numerical simulation and physical tests, the author tried to propose a segmental power function damage model and determine the distribution rule of cohesive stress of equivalent crack according to the model. The expressions of concrete initial fracture damage threshold, as well as the ultimate length of the fracture process zone were derived. The crack growth process of three-point bending concrete beams with and without original cracks was simulated using numerical methods. And then the feasibility and validity of numerical solving method with D-K model were verified. Finally, the influence of initial ao/D on unstable fracture toughness, KIc was discussed.
It is a homogenization process for concrete from meso multiphase structure to macroscopic uniform material, the quantitative relationship between the meso composition and macroscopic properties can be reflected by homogenization. Based on inclusion theory of composite materials, a mixture inclusion model for concrete was put forward, the analytical solution for the model was derived with generalized self-consistent and Mori-Tanaka method. The elastic modulus of concrete was predicted using this model, the main influencing factor such as aggregate volume percentage, interface thickness, elastic modulus, content of void and micro cracks were analyzed.
引文
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