TALLER – DISEÑO DE MEZCLAS DE CONCRETO
Ligia María Vélez Moreno
Ing. Civil
Esp. Docencia universitaria
Esp. Ingeniería Sismorresistente
Profesora Asociada ITM
Investigadora
ligiavelez@itm.edu.co
ligiamariavelezmoreno@yahoo.es
Tel (57)(4)4405178
- OBJETIVOS DEL DISEÑO DE MEZCLAS DE CONCRETO
Determinar la combinación más práctica (factible de realizar), económica, satisfacción de requerimientos según condiciones de uso en los sistemas constructivos, para hacer edificaciones durables, y lograr eficiencia en los procesos constructivos tanto en obra como en planta.
- CARACTERISTICAS DE LOS MATERIALES PARA UN DISEÑO DE MEZCLAS
2.1 Granulometría de los agregados, favorece la gradación o acomodamiento de los agregados partículados en la masa de concreto, y se relaciona con la cantidad de superficie en la interfase con la pasta de cemento en la mezcla en estado fresco.
2.2 Modulo de finura de los agregados, es la proporción de los valores de retenidos acumulados en el tamizaje hasta e incluido el tamiz 100, dividido por 100, condiciona el tipo de concreto como concreto de agregados gruesos (ciclópeo), agregados medios (normal), agregados finos (liviano), además de las condiciones superficiales y efecto terminal como concreto arquitectónico.
2.3 Densidades aparentes de los agregados, las densidades aparentes incluyen la humedad normal de los agregados con porcentajes de humedades en los poros de las partículas de los agregados sobre el volumen total del agregado. Es la característica principal para optimizar tiempos de mezcla, tiempos de fraguado y curado de las mezclas, como también en el proceso constructivo los empujes a tener sobre las superficies de contacto en la obra falsa de los encofrados de los elementos de concreto.
2.4 Absorciones de los agregados, determinante de la capacidad de adhesión mecánica entre la superficie de los agregados y la pasta de cemento, y como consecuencia propiedades mecánicas como la resistencia a la compresión, a la tensión y dureza del concreto terminado.
2.5 Masas unitarias de los agregados, las masas de los agregados por unidad de volumen , relaciona la capacidad de acomodamiento de los agregados, en el caso de las densidades compactadas, y las densidades en estado aparentemente seco las condiciones de manejabilidad y consistencia de la mezcla de concreto en estado fresco.
2.6 Humedades de los agregados, las humedades se convierten en el factor modificador de la relación agua cemento de las mezclas para evitar excesos de fluidez y consistencias inmanejables en las mezclas frescas.
2.7 Tipo de cemento y Densidad del cemento, el tipo de cemento según las condiciones especiales de uso al elemento constructivo que se ejecuta., y su densidad para corroborar con exactitud su consumo por metro cúbico a construir o por kilogramo a vaciar.
- RELACIONES IMPORTANTES ENTRE LAS CARACTERISTICAS
Uso concreto | asentamiento cm | tipo de concreto | consistencia | TMN | f¨c Mpa | A/C | b/b0 | cont aire % | agua mezclado |
tipo de estructura y condiciones de colocacion | | | | | | del concreto a los 28 días | | | | |
Vigas y pilotes de alta resistencia, con vibradores de formaleta | 0,0 | 2,0 | concreto común | media | 1/2" | 21 | 0,5 | 0,59 | 2,5 | 0,13 |
Pavimentos vibrados con máquina mecánica | 2,0 | 3,5 | concreto comun +agregado grueso | alta | 3/4" | 28 | 0,42 | 0,64 | 2 | 0,145 |
Masa voluminosas, losas medianamente reforzadas, fundaciones concreto simple,pavimentos con vibradores normales | 3,5 | 5,0 | concreto comun, concreto ciclopeo, concretos de gravedad | alta | 1"-11/2" | 28 | 0,42 | 0,67-0,69 | 1,5-1,0 | 0,16 |
losas y pavimentos reforzados y compactados a mano. Columnas, vigas, fundaciones,y muros con vibración | 5,0 | 10,0 | concreto ciclopeo, concreto comun | alta y media | 1" | 21 | 0,5 | 0,67 | 1,5 | 0,175 |
Secciones con mucho refuerzo, revestimiento de tuneles, no recomendable para demasiada vibración. | 10,0 | 15,0 | concretos livianos, concreto comun | alta | 1/2"-3/4" | 35 | 0,35 | 0,59-0,64 | 2,5-2,0 | 0,185 |
International Journal of Fracture
84: 159–173, 1997.
c
1997 Kluwer Academic Publishers. Printed in the Netherlands.
Correlation of fatigue crack propagation in polyethylene pipe
specimens of different geometries
A. SHAH
1, E.V. STEPANOV1, A. HILTNER1 , E. BAER1 and M. KLEIN21
Department of Macromolecular Science, Case Western Reserve University, Cleveland, OH 44106, U.S.A.2
900G 24th Street N.W., Washington, DC 20037, U.S.A.Received 16 September 1996; accepted in revised form 18 February 1997
Abstract.
Correlation in mechanisms and kinetics of step-wise fatigue crack propagation in polyethylene pipespecimens of different geometries is studied experimentally. It is shown that crack propagation in a non-standard
specimen cut from a real pipe and conserving the pipe geometry can be effectively simulated using a standard
compact tension specimen. Good correlation in both kinetics of step-wise crack propagation and fractography
between the specimens is achieved if experimental conditions are chosen to assure equal values of (a) stress
intensity factor and (b) stress intensity factor gradient at the initial notch tips. These results extend previous
technique of fatigue accelerating slow crack growth used to predict lifetime of polyethylene pipes.
Key words:
fracture, fatigue, polyethylene, crack propagation, accelerated failure.1. Introduction
With increasing use of polyethylene pipes for gas distribution, an application which requires
structure integrity for decades, the problem of predicting long-term reliability of the pipes
becomes important. Because very long lifetimes are desired, testing under exact field conditions
becomes impossible. This is the motivation for developing experimental and theoretical
procedures for predicting long-term lifetime and ranking pipe materials on the basis of shortterm
experimental tests. Numerous investigations performed during the last decade show that
the slow crack propagation mechanism that causes the majority of pipe field failures can be
simulated in the laboratory using either creep at elevated temperatures or fatigue to accelerate
failure [1–7]. The experiments reproduce the main features of the field failure such as periodical
arrest and step-wise character of crack propagation [8], and therefore can be the basis for
scaling short-term test results for lifetime assessment [9–17].
A recent study [16] found direct phenomenological correlation between fatigue and creep
crack propagation rates. The correlation was obtained by measuring the crack growth rate at
gradually increasingmagnitude of the fatigue ratio
R (minimum load to maximumload) whenkeeping the mean load constant. Extrapolation to the creep condition
R = 1 utilized a Parisequation for fatigue, and a similar power law dependence reported for creep crack growth
in polyethylene pipe material [15]. This makes the much more rapid fatigue test practically
equivalent to the creep test.
Failure in the creep test, especially for the most recent materials, can require many months
[18, 19]. The fatigue test, on the other hand, can accelerate the failure time by up to three
orders of magnitude over the creep test; resulting failure times become a matter of days or
hours rather than months [9, 17, 19]. The fatigue test also has the advantage of avoiding
To whom correspondence should be addressed.160
A. Shah et al.the significantly elevated temperatures used in the accelerated creep test, and the concomitant
possibility of annealing effects especially as themelting point is approached.Therefore fatigue
may be the only way to test some recently developed novel high-resistant pipematerials where
creep test times are so long as to be impractical [17–19].
For proper fatigue simulation of crack growth in a real pipe, a number of specific requirements
have to be met in the specimen design. One is related to the effect of process history
on pipe material morphology, and hence on the effect of fatigue. This requires the tested
specimens to be prepared from a real pipe, and to be notched and loaded in a way that simulates
crack propagation in a real pipe. A technique for fatigue testing arc-shaped specimens
that are cut from a real pipe and that conserve the pipe geometry has been described [4, 5,
9]. However, due to the comparatively low elastic modulus of pipe materials, non-standard
arc-shaped specimens experience perceptible deformation upon loading which changes the
elastic stress distribution. This presents difficulties in analyzing the test data and comparing the
results for pipes of different dimensions. Testing experimental materials for pipe applications
is also hampered in this way. On the other hand, the standard procedure for characterizing,
comparing and ranking polymeric materials with respect to their fracture toughness is based
on standard specimens such as compact tension [20] as well as single-edge-notched [7, 18,
19], and central-crack-tensile [21] specimens where the stress concentration is well described
by the usual methods of fracture mechanics, and where sample geometries are accurately
reproducible. To be able to predict the pattern of fatigue crack propagation (FCP) in a real
pipe fromresults of standard tests, it is necessary to develop correlations between FCP in specimens
of different geometries prepared from the same polyethylene material, one of which is
a standard, well-defined geometry such as the compact tension specimen. This is the subject
of the present article.
2. Approach to correlating geometries for FCP
In the brittle regime of FCP, while the remote stress is much less than the yield stress
Y andthe plastic (craze) zone is small, the local elastic stress distribution in the vicinity of the crack
tip is described by the stress intensity factor
KI. Thus we suppose that if we attain the samevalue of
KI at the tip of the initial notch in two different specimen geometries of the samematerial, and if, in both cases, this value does not change very much as the crack grows, then
the craze zone is developed by the action of the same local stress field, and the kinetics and
mechanism of crack propagation will be similar.
For the specific geometries of interest, which have different and non-uniform elastic fields,
the change of the stress intensity factor
KI with distance fromthe initial notch (theKI gradient)can significantly affect the initial crack growth rate. Qualitatively, this is caused by both the
finite length of the plastic (craze) zone (
l) and the strong dependence of the crack growthrate (
w) on stress intensity factor. The condition that the stress intensity factor gradient doesnot affect
w at a given point is that the crack growth rate does not change appreciably overa distance on the length scale of the craze zone. If we assume the ordinary Paris dependence
for the crack growth rate (
w / (KI)m / (KI; max)m, where KI = KI;.............................................
for........
6. Results
Fracture surfaces for both compact tension and real-pipe specimens showed striations indicating
step-wise crack propagation (Figures 5, 6). The discontinuous crack growth bands,
confined between the striations (the crack arrest lines), began from the notch and gradually
increased in size. Further from the notch, as the stress increased, arrest lines blunting occurred
and characteristics of high deformation ductile tearing were observed. Crack propagation was
investigated only in the ‘brittle’ step-wise region and the tests were stopped when ductile failure
initiated. A typical plot of the crosshead displacement during testing of a CT specimen is
shown in Figure 7. The step-wise character of crack growth is well resolved on the plot where
the number of plateau periods correlates with the number of the bands on the fracture surface,
and the sharp increases in crosshead displacement indicate the discontinuous crack jumps.
The rate of crack growth was determined by dividing the crack jump length by the number
of cycles between consecutivemembrane ruptures. The crack jump length wasmeasured from
the distance between the fatigue striations. The number of cycles between membrane ruptures
was obtained both from the crosshead displacement vs. time curve and from the videorecord
of crack propagation. As seen in Figure 7, the number of cycles for membrane rupture was
small (5,000–10,000) compared to the number of cycles between membrane ruptures (60,000)
and therefore could be neglected. The crack growth rate (d
a/dN) is plotted vs. stress intensityfactor range,
KI, defined as the difference between KI; max and KI; min. Figure 9 comparesthe crack growth rate in CT and RP specimens tested at the same values of
KI andKI gradient.Overlap of the data indicates correlation in fatigue crack propagation kinetics. Because the
data are plotted on a double logarithmic scale, the straight line defines a Paris relationship
where the slope is usually considered to be a characteristic of the material. A regression line
through the data gives a value of 4
:0 0:5, which is typical for polyethylenes [26].In summary, correlation of stress intensity factor and its gradient was sufficient to achieve
correlation in the mechanism and kinetics of fatigue crack propagation in specimens of
different geometries. The correlation allows one to simulate fatigue failure in a real pipe
using specimens of standard geometries. Furthermore, using established methodology [16],
the fatigue results can be the basis for lifetime predictions for polyethylene pipe.
Acknowledgments
The authors are grateful to G. Capaccio and A. Moet for the many useful discussions that
resulted fromtheir sustained interest in thiswork. The researchwas funded by the GasResearch
Institute (contract number 5090-260-2031). The financial assistance of BP Chemicals Ltd. is
also gratefully acknowledged.
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