A.H. Marchertas

CONCRETE MODEL WITH NORMALITY AND SEQUENTIAL IDENTIFICATION

Abstract To facilitate numerical finite element analysis, it is desirable to endow the constitutive model with normality, associatedness, continuity, convexity and absence of corners. Although these mathematical conditions represent only crude approximations of the actual behavior of concrete, it is of interest to find the best possible constitutive model which meets these conditons. This is one objective of the present paper. The second objective is to develop a model which permits a simple identification of material parameters from test data. The material parameters need not be obtained by simultaneous nonlinear optimization of the fits of all data. Rather, they are obtained in sequence through a precisely defined procedure which involves solving two systems of linear equations. The model describes not only hardening but also post-peak softening under various triaxial stress states. The model agrees well with the available basic test data from monotonic loading tests.

Analysis and application of prestressed concrete reactor vessels for LMFBR containment

Abstract An analytical model of a prestressed concrete reactor vessel (PCRV) for LMFBR and the associated finite element computer code, involving an explicit time integration procedure, is described. The model is axisymmetric and includes simulations of the tensile cracking of concrete, the reinforcement, and a prestressing capability. The tensile cracking of concrete and the steel reinforcement are both modeled as continuously distributed within the finite element. The stresses in the reinforcement and concrete are computed separately and combined to give an overall stress state of the composite material. The reinformcement is assumed to be elastic, perfectly-plastic; the concrete is taken to be elastic, with tensile and compressive stress limits. Cracking of concrete is based on the criterion of maximum principal stress; a crack is assumed to form normal to the direction of the maximum principal stress. Attention is also given to the fact that cracks do not form instantaneously, but develop gradually. Thus, after crack initiation the normal stress is reduced to zero gradually as a function of time. Residual shear resistance of cracks due to aggregate interlock is also taken into account. An existing crack is permitted to close. Prestressing of the PCRV is modeled by special structural members which represent an averaged prestressing layer equivalent to an axisymmetric shell. The internal prestressing members are superimposed over the reinforced concrete body of the PCRV; they are permitted to stretch and slide in a predetermined path, simulating the actual tendons. The validity of the code is examined by comparison with experimental data. Both static and dynamic data are compared with code predictions, and the agreement is satisfactory. A preliminary design has been developed for both pool and loop-type PCRVs. The code was applied to the analysis of these designs. This analysis reveals that the critical locations in such a design would be the head cover and the junction between the cover and the vessel wall and indicates the pattern of crack development. The results show that the development of a design adequate for current HCDA loads is quite feasible for pool-type or loop-type PCRVs.

Thermo-mechanical analysis of concrete in LMFBR programs

Abstract The R&D program described in this paper represents the structural mechanics effort underway and planned at ANL as an attempt to better understand the behavior of concrete structures in LMFBR plants where such structures are subjected to high temperature levels. This paper describes the analytical tools formulated and incorporated into the thermo-mechanical computer code called TEMP-STRESS. Emphasis in this paper is placed on describing the short-time and long-time constitutive formulation for concrete. The primary constitutive relation uses an elasto-plastic technique to simulate concrete nonlinearities, utilizes the von Mises ellipsoid as the loading surface, and assumes a four-parameter failure surface. Post-failure treatment is different when considering surface elements as opposed to internal elements. Creep of the concrete at temperatures up to about 400°C is approximated by a rate-type creep law using Maxwell chain technique. The creep model accounts for moisture and pore pressure disposition of the concrete.

Numerical modeling of concrete under thermal loads

Abstract The formulation needed for the conductance of heat by means of explicit integration is presented. The implementation of these expressions into a transient structural code, which is also based on explicit temporal integration, is described. Comparisons of theoretical results with code predictions are given both for one-dimensional and two-dimensional problems. The coupled thermal and structural solution of a concrete crucible subjected to a sudden temperature increase predicts the history of cracking. The extent of cracking is compared with experimental data.

Dynamic response of fast-reactor core subassemblies☆

Abstract A program for predicting the behavior of the hexagonal fuel assembly duct when subjected to internally generated pressures in the LMFBR is described. To a large extent, studies have been made with two-dimensional models of the hexcan. In these problems, the loadings must be restricted to line loads of sufficient length so that axial effects can be neglected. The finite element models range from a single hexcan to models which include both the loaded hexcan, two adjacent rows of hexcans, the coolant layers between hexcans, and the fuel rod assemblies. A nonlinear, transient finite element program called STRAW is used for the analyses. The program accounts for both geometric and material nonlinearities, and has special features for treating the coolant layer between hexcans by a quasi-Eulerian description and vertical flow in the hexcans and layer so that motions of the coolant can be accurately analyzed. The model has been used with loadings ranging from 500 psi to the kilobar range, and has yielded significant results on damage in adjacent assemblies and the restraining effects of the coolant. For example, preliminary results have shown that deformations of the loaded hexcan are reduced by 25 to 50% when the role of the coolant is included and that corner ductility has very large effects on hexcan response.

Concrete cracking simulations for nuclear applications

Abstract The need to understand concrete behavior under high temperatures in the nuclear industry has become rather acute. Previously, concrete has been used in nuclear industry as inexpensive material for construction and also for radiation shielding. Presently, we are concerned with the structural integrity of the containment, subject to accidental exposure of concrete to excessively high temperatures and chemical attack. Consequently, we are now seeking basic understanding of concrete behavior at extreme environmental condition. Indispensible in mathematical modeling of concrete behavior is the constitutive relation. A constitutive model developed by Takahashi [1] has been incorporated into the coupled thermal-stress analysis code, TEMP-STRESS, which gives the stress-strain relation up to the point of cracking. This paper describes the modeling of cracking behavior. Four crack propagation criteria: the J-integral, the energy release rate, the effective strength and the failure surface criterion are examined. Several numerical examples are given. Situations under which one method might be more convenient to use than the others are discussed.

Reinforced flexural elements for TEMP-STRESS program

Abstract The implementation of reinforced flexural elements into the thermal-mechanical finite element program TEMP-STRESS is described. With explicit temporal integration and dynamic relaxation capabilities in the program, the flexural elements provide an efficient method for the treatment of reinforced structures subjected to transient and static loads. The capability of the computer program is illustrated by the solution of several examples: the simulation of a reinforced concrete beam; simulations of a reinforced concrete containment shell which is subjected to internal pressurization, thermal gradients through the walls, and transient pressure loads. The results of this analysis are relevant in the structural design/safety evaluations of typical reactor containment structures.

Increasing Primary Containment Capabilities of Liquid-Metal Fast Breeder Reactor Plants by the Use of Prestressed Concrete

The Argonne National Laboratory developed computer program DYNAPCON for the transient analysis of a prestressed concrete reactor vessel (PCRV) for liquid-metal fast breeder reactor (LMFBR) primary containment is applied to a reference design concept representative of large, pool-type LMFBR reactor plants. Estimates of the energy absorption capability of a PCR V primary containment vessel are provided to assist in the establishment of the engineering feasibility of such a design concept. The reference design analyzed utilizes existing concrete stnlctures already in place for biological shielding and component support. The very large

Pretest analysis of a 1:6-scale reinforced concrete containment model subject to pressurization

Abstract Pretest predictions were made by the Reactor Analysis and Safety Division of Argonne National Laboratory for the response of the 1 :6-scale reinforced concrete model to be tested by Sandia National Laboratories. For this purpose a series of axisymmetric models were studied with the two-dimensional computer program TEMP-STRESS and a three-dimensional circumferential segment model with the program NEPTUNE. The two-dimensional models predicted failure at 175–190 psig (1.207–1.310 MPa). However, two different failure mechanisms were indicated: (1) hoop failure of the vessel at midheight following failure of a splice in this area, (2) failure of a weld in the liner near the basemat due to excessive strains. The three-dimensional model predicted failure at an internal pressure of 180–185 psig (1.241–1.276 MPa) by failure of the splices of the hoop rebars just above cylinder midheight in a region away from the equipment hatch opening.

Damage-plastic loading surface model for concrete

Abstract The paper presents a plasticity-type model which is characterized by normality, continuity, convexity and associatedness. It utilizes two loading surfaces, of which one describes the behavior associated with damage due to inelastic volume change (expansion from micro-cracking, or contraction from pore collapse or closure) and the other plasticity at no inelastic volume change. Since only one of these two surfaces is active at the same time, the formulation is equivalent to a single loading surface. The deviatoric section of the damage loading surface is a rounded triangle, and the Rendulic section meridians have the shape of a slanted ellipse. The loading surfaces are smooth and have no corners. Although the model involves approximately the same number of material constants as the previous models of similar capability, identification of these constants from test data is much simpler. The properties of the model are also more advantageous for numerical finite element applications. The model is shown to be capable of describing the basic uniaxial and multiaxial test data for concrete except degradation of material stiffness.