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Submitted on 1 Jan 1985
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APPLICATION OF A NEW TECHNIQUE TO STUDY THE DYNAMIC TENSILE FAILURE OF CONCRETE
J. Gran, L. Seaman, Y. Gupta
To cite this version:
J. Gran, L. Seaman, Y. Gupta. APPLICATION OF A NEW TECHNIQUE TO STUDY THE DY NAMIC TENSILE FAILURE OF CONCRETE. Journal de Physique Colloques, 1985, 46 (C5), pp.C5 617C5622. �10.1051/jphyscol:1985579�. �jpa00224813�
JOURNAL DE PHYSIQUE
Colloque C5, supplement au n08, Tome 46, ao0t 1985 page C5 6 1 7
APPLICATION OF A NEW TECHNIQUE TO STUDY THE DYNAMIC TENSILE FAILURE OF CONCRETE
J.K. Gran, L. Seaman and Y.M. ~ u ~ t a *
SRI International, 333 Ravenswood Avenue, Men20 Park, CA. 94025, U.S.A.
*washington S t a t e University, Department of Physics, Pullman, WA. 99163, U.S.A.
Rgsum6: Une nouvelle technique pour soumettre le bgton 1 la traction dyn?m?qu: est d6crite. Les rgsultats d'un essai sont interpretes a l'aide de simulations num&iques.
Abstract: A new technique to test concrete in dynamic tension is described. The results of an experiment are interpreted using numerical simulations.
INTRODUCTION
Tensile failure in concrete is produced by the nucleation, growth, and coalescence of microcracks. The tensile strength is the stress at which this process of accumulating damage becomes locally unstable. Once the material has become unstable, it quickly loses its resistance to further deformation. An ideally brittle material would lose all its strength instantaneously. In real materials the strength reduction is a function of further accumulating tensile damage and requires a finite time to occur.
The objectives of this work were to develop and demonstrate experimental and analytical techniques to obtain a measure of the tensile strength and of the strength reduction as a function of accumulating tensile damage, for concrete at strain rates on the order of 10 per second. First, experiments were conducted in which concrete rods were subjected to dynamic tension, and the effect of tensile failure was measured in surface strains. Then the experiments were interpreted with a simple elasticfracturing model using finite difference calculations.
EXPERIMENTAL TECHNIQUE
The concept of the experiments is shown in Figure 1. Rods measuring 5 cm in diameter and 76 cm in length are first loaded hydraulically in static triaxial compression. Then the axial pressure is released from each end simultaneously and very rapidly, using explosive charges to free lightweight pistons. The resulting relief waves propagate to the center of the rod and superpose to produce a dynamic tensile stress equal to the original static compression. Tensile failure occurs near the midpoint of the rod if the static compression exceeds the dynamic tensile strength. The radial pressure is held constant during the experiment. The apparatus is capable of applying up to 20 MPa pressures with an unloading time of about 30 ps.
The end pressure histories and the confining pressure are measured during the experiment. Axial and circumferential surface strains are also measured at several locations along the length of the rod.
As an example, we describe a dynamic tension test of a concrete rod with no
confinement and a static uniaxial preload of 10.55 MPa. The static uniaxial tensile
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985579
C5618 JOURNAL DE PHYSIQUE
FIGURE 1 DYNAMIC TENSILE LOADING DEVICE
strengthr1] of the concrete was about 3.5 MPa, and the static uniaxial compressive strengthr2] was about 50 MPa. The static elastic modulus was 24.1 GPa; Poisson's ratio was 0 . 2 . ~ ~ ~ The rod failed in dynamic tension at a single location, 0.46 cm from the midpoint, and no secondary damage was visible.
The fracture surfaces, shown in Figure 2, passed through the mortar, voids in the mortar, mortar/aggregate interfaces, and some of the larger aggregates.
JP445145 FIGURE2 FRACTURESURFACES INTEST42
[ll~he tensile strength was determined from splitcylinder tests on samples taken from the rod after the dynamic tension test.
i2]~he compressive strength was determined from tests on specimens taken from a companion rod.
131~he elastic constants were determined from the measurement of the static axial preload and the average initial strains.
The axial strains at f7.6 cm from the midpoint of' the rod are shown in Figure 3. In the time scale of these plots, the explosive charge was initiated at t = 0.100 ms.
Three 2.5cmlong strain gages were mounted at 120degree spacing at each location.
All the strain records were scaled to correspond to the average static elastic moduli.
0.25 0.3 0.35 0.4 0.45 0.5 0.25 0.3 0.35 0.4 0.45 0.5
TIME (ms) TIME (ms)
(a) 7.6 cm (7.1 cm from the fracture) (b) 7.6 crn (8.1 cm from the fracture)
JA445139A
FIGURE 3 AXIAL STRAINS MEASURED + 7.6 cm FROM THE MlDPOlNl
At both locations, the strains are fairly uniform even after the effects of tensile failure arrive. The effects of dispersion are noticeable in the axial strains at k7.6 cm at the beginning of the pulse. At about t = 0.380 ms, these strains show the effect of tensile failure.
The strain rate at the front of the fracture signals is about 10/s, so the strain rate at the failure location, where the two wave fronts superposed, was about 201s.
At 7.6 cm, 7.1 cm from the failure location, the peak average strain was 160 microstrain. At +7.6 cm, 8.1 cm from the failure location, the peak average strain was 210 microstrain. The elastic axial stress computed from the highest measured strain is about 5 MPa, more than 40% higher than the static splitting tensile strength. However, the inelastic analysis described below shows that these measured strains are not totally elastic.
INTERPRETATIONS OF THE EXPERIMENTS
The purpose of the analyses conducted in this study is to provide a? interpretation of the experimental results. In particular, the objective is to estimate for each experiment the tensile strength and the strength reduction as a function of accumulating damage at the observed failure locations. We are not creating a constitutive model at this stage; we are merely attempting to extend the data base by estimating a response that cannot be measured directly. To do this, an elastic fracturing material behavior is assumed. Then, using numerical simulations, we can identify the set of input parameters providing the best match to the experimental observations.
The analytical model used for tensile failure is simply a prescribed relation between the stress at the failure location and the fracture volume created during the failure process. The concept of the model is illustrated in Figure 4. The initial elastic modulus is that of intact material, and fracture volume is assumed to first increase only when the stress reaches the tensile strength. As the
fracture volume increases to a critical value, the strength is reduced to zero. The relation between stress and fracture volume can be chosen arbitrarily. Unloading can be prescribed to be elastic or inelastic.
JOURNAL DE PHYSIQUE
Fracture Volume Critical ~racture Volume Per Unit Area ( 6 ) Per Unit Area (6,) (a) Elastic Straining Up (b) Growth of Fracture Volume (c) Tensile Failure
to Critical Stress
JA445168 FIGURE 4 CONCEPT OF THE TENSILE FAILURE MODEL
When implemented as a stressstrain relation, the strain value corresponding to complete separation will depend on the original dimensions of the fracturing cell.
That is, for a given stress versus fracture volume relation, the stress versus strain relation depends on the cell size used in the numerical discretization.
Interpreted literally, the cell size in this model is equivalent to the allowed crack spacing. Each cell represents a failure plane surrounded by elastic material.
This notion suggests that there may be a correct, or best, cell size consistent with the actual average spacing of damage planes produced in the experiments.
Determining the average crack spacing (cell size) experimentally would require microscopic inspection of the material, possibly timeresolved microscopic
inspection. This kind of information is not available. Therefore, we have endeavored to find, by trial and error, the cell size and failure parameters that produce the best match to the observed surface strains.
In the simulation of an experiment, tensile failure was forced to occur at the observed locations of failure by degrading the properties of the rod at those locations. The initial strength at the fracture locations was at least 80% of the strength in the rest of the rod. The measured elastic constants and the measured density were used as input to the calculation.
The relations for stress versus fracture vol6me per unit area, and for stress versus strain, used in the simulation of the experiment described above are shown in Figure 5. The strength in the rod was 4.4 MPa, 30% higher than the static splitting strength. The critical fracture volume per unit area was about 5 pm. The strength in the cell at the fracture location, 0.46 cm from the midpoint of the rod, was degraded to 3.5 MPa (80% of the strength in the rest of the rod) to produce total separation only at the desired location. The 1 MPa difference between the two curves was needed to prevent multiple fractures. The strength levels were &osen to get the best agreement with the peak strains. The initial softening slope of the stress versus fracture volume relation for the rod was chosen to match the rounded peaks in the strain histories. The critical fracture volume was chosen to match the pulse duration and to prevent multiple fracture.
The simulation shown below was performed using 0.635cm cells. This cell size was found to be most suitable. When 0.333cm cells were used, the roundness of the measured strain history peaks could not be matched because the calculated strain histories were too flat. When 1cm cells were used, additional fractures would occur in the rod.
The comparisons of calculated and measured strains at f7.6 cm are shown in Figure 6.
As the comparisons of strain histories show, this combination of failure parameters and cell size produces a very good match to the experimental results.
I I I I I I I I I * This Slope Needed
for Rounded Peak
 
Peak Strain Remote rn Fracture (Test 42)

 This Ductility Needed
for Pulse Duration
1 1 1 1 
FIGURE 5 STRESSSTRAIN RELATIONS USED TO SIMULATE TEST 42 (0.635cm CELLS)
(a) X = 7.6 crn (b) X = 7.6 crn
400
2
200* + ^{0 }
0 a
0 200 H
400
FIGURE 6 CALCULATED AND MEASURED STRAINS FOR TEST42
! ' , '
 
 Measured 

 
I , I . I .
The calculated peak strains for this case are shown in Figure 7. At the locations of the strain gages, the inelastic strain was slight. Thus, the assumption that the measured peak strains were elastic would give a reasonable approximation to the strength. However, inelastic strain occurred nearly everywhere in the rod, so a strictly elastic analysis would not be appropriate. In particular, damage was concentrated at two locations about 3 cm from the fracture. The magnitudes of these peaks imply that less than half of the unrecovered work done was energy released at the fracture location.
0.3 0.35 0.4 0.45 0.5 0.25 0.3 0.35 0.4 0.45 0.5
TIME (ms) TIME (rns)
JOURNAL DE PHYSIQUE
1000 1 I I 1 I
Fracture Location
4
^{I }Strain Gage ^{I } ^{I }
Locations ^{i } y
r
i ! , I
FIGURE 7 PEAK STRAINS CALCULATED FOR TEST 42 Elastic peak strains are not shown.
CONCLUSIONS
The experimental techniques developed and demonstrated in this research effort provide a new method for studying the dynamic tensile response of concrete and, possibly, many geologic materials. In its present configuration, the tensile testing apparatus will produce up to 20 MPa tensile stress with up to 20 MPa confining stress at a strain rate of about 201s. The primary failure location occurs within a few centimeters of the midpoint of the rod, and surface strains measured a few centimeters away capture the effects of tensile failure on stress waves in the specimen.
In the analyses, the stress versus fracture volume relations and the cell size were chosen to produce the best match to the strain measurements. The input to the calculations is the best estimate of the apparent concrete properties in these experiments. The failure parameters used to get the best match with the data certainly cannot be considered unique, but our experience is that there is not much latitude in the choice of the model parameters that produce a good match with the measurements. Based on these analyses, the unconfined strength of the concrete at a
strain rate of 201s is about 4.4 MPa, 25% higher than the static splitting strength. The stress versus fracture volume relation is not linear, and the critical fracture volume per unit area is about 5 pm. The natural crack spacing is about 0.635 cm.
ACKNOWLEDGMENT
This work was supported by the U.S. Air Force Office of Scientific Research under Contract No. F4962082K0021.