MIXED-MODE CRACK PROPAGATION
IN MORTAR AND CONCRETE
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment for the Degree of
Master of Science
by
Manrique Arrea
January 1982
ABSTRACT
A combined experimental and analytical investigation into mixed-mode crack
propagation in mortar and concrete was undertaken. The experimental program
consisted of tests on three series of beams under a four-point loading system
that created a high KII/KI ratio at the tip of a sawed-in notch. As the crack
propagated from the notch, this ratio decreased as the Mode I stress intensity
factor began to dominate. This allowed the determination of peak loads, crack
extensions, compliances, crack mouth sliding displacements and final crack
trajectories in a varying mixed-mode stress field at the tip of the growing
crack.
A continuous load versus crack mouth sliding displacement record was obtained
for comparison with the numerical analysis. The loading of the beams was
cyclic to obtain several compliance values for each beam. The crack lengths
were located and measured on each side of the beams with the aid of
fluorescent dye penetrant, ultraviolet light and microscopes. The final crack
trajectories on each beam were traced at the end of the test.
The experimental program was followed by a finite element analysis which
implemented existing mixed-mode fracture initiation theories. The principal
objective was to determine whether mixed-mode, linear elastic fracture
mechanics applies to mortar and concrete.
Crack propagation in the numerical analysis was based on an energy balance
between G, potential energy release rate, and R, material's resistance to
crack growth. The Mode I and Mode II stress intensity factors, KI and KII,
respectively, were determined from a displacement correlation method.
Necessary fracture toughness values were obtained from pure Mode I testing of
beams of the same geometry and material composition. An aggregate interlock
model was included in the analysis, providing both shear and normal stiffness
to the crack surfaces.
The behavior of the beams up to peak load was reproduced satisfac- torily by
the numerical analysis only when aggregate interlock effects were included.
However, an error in the program hindered the modeling of the post-peak
behavior when interface elements were included. Of the three mixed-mode
fracture initiation theories implemented in the code, the S(Theta)min theory
predicted the initial instability loads that best resembled experimentally
recorded loads. Loads and respective crack mouth sliding displacements were
accurately predicted, as well as the beams increasing compliance as the crack
propagates. Crack trajectories observed in the tests were accurately
reproduced with the numerical analysis.
Although the present investigation was limited in terms of variation in crack
geometries and material properties, results strongly suggest that mixed-mode,
linear elastic fracture mechanics can be applied to concrete. More research in
this field is necessary and recommended to overcome limitations encountered in
this investigation.
CONCRETE FRACTURE: A LINEAR ELASTIC
FRACTURE MECHANICS APPROACH
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment for the Degree of
Master of Science
by
David Michael Catalano
January 1983
ABSTRACT
An experimental and numerical investigation of mode I crack propagation in
mortar and concrete was undertaken. The principle objective was to determine
whether Linear Elastic Fracture Mechanics (LEFM) is applicable to, and thus
characterizes the fracture behavior of, mortar and concrete.
The experimental program consisted of one mortar and two concrete series of
beams tested in three-point bending, in accordance with ASTM Standard E399.
The loading was cyclic, so that a series of compliance and apparent fracture
toughness values could be determined for crack lengths ranging from 3 to 10 in (76.2 to 254 mm).
The numerical investigation consisted of finite element analyses of the
three-point bend specimen, to produce compliance and apparent fracture
toughness versus crack length relationships. These analyses were performed
with and without account taken of the presence of tractions in the crack. The
former case was analyzed because the aggregate particle sizes in the mortar
and concrete tested were found to be much larger than the crack widths that
developed in the test specimens, thereby linking the two opposing crack
surfaces and transferring stresses.
It was found that neglect of the presence of aggregate particles bridging the
crack (termed an interface) produced diverging experimental and numerical
compliance versus crack length relationships. Furthermore, apparent fracture
toughness values computed using ASTM Standard E399 increased rapidly with
increasing crack length. This occurred because these apparent fracture
toughness values are a measure of both the energy required for crack tip
process zone formation, plus the energy required to displace the interface.
Since the interface lengthened as the cracks propagated, the apparent fracture
toughness values had to follow suit. Although not seen in this investigation,
the interface must eventually attain a maximum length (depending on the
geometric configuration of the test specimen), and thus the apparent fracture
toughness must reach an asymptotic value. This value can be as high as 4.5
ksiĂin (4.94 MPĂm).
When the presence of an interface is incorporated into the finite element
analyses, there is excellent agreement between experimental and numerical
compliance versus crack length results. Moreover, the apparent fracture
toughness values remain constant with increasing crack length. These values,
in the range of 0.45 ksi Ăin (0.49 MPaĂm) to 0.85 ksi Ăin (0.93 MPaĂm), are
material properties of the mortar and concrete tested, and they characterize
the energy needed for crack tip process zone formation. The crack tip process
zone size is on the order of 1/2 in (12.7 mm), while the total process zone
size (i.e., the crack tip plus the interface) can be as high as 12 in (305
mm).
The conclusion reached was that a LEFM parameter, KIC, is a meaningful and
viable criterion for predicting crack propagation in materials such as mortar
and concrete, provided the presence (in the case of natural cracks) or the
absence (in the case of cast or sawn sharp notches) of an interface is duly
accounted for.
THE FRACTURE MECHANICS OF BOND
IN REINFORCED CONCRETE
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment for the Degree of
Master of Science
by
Walter Herbert Gerstle
August 1982
ABSTRACT
Fracture mechanics concepts are used in the analytical investigation of
bond-slip in reinforced concrete. A computer program developed at Cornell
University, Finite Element Fracture Analysis Program (FEFAP), was the
principal tool used in the analyses.
Initially, linear elastic fracture mechanics principles were used in
determining cracking behavior at the steel-concrete interface. hen analytical
results were compared to experimental data, this approach was found to be
inadequate. Subsequently, nonlinear fracture mechanics theories were used in
the analysis of the bond-slip problem. These nonlinear fracture mechanics
theories were programmed into the crack propagation algorithm of FEFAP.
As a result of this anlaytical investigation, the cracking behavior of bond
became more clearly understood. In particular, the interaction between primary
and secondary cracks in reinforced concrete structures became apparent.
Finally, a "tension-softening" finite element was proposed and tested in a
hypothetical problem. This element lumps all bond-slip behavior into a single
nonlinear finite element. The "tension-softening" element provides a
significant simplification in the finite element modelling of bond-slip in
reinforced concrete.
INTERACTIVE FINITE ELEMENT ANALYSIS OF FRACTURE PROCESSES:
AN INTEGRATED APPROACH
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by
Paul Andrew Wawrzynek
May, 1987
ABSTRACT
This thesis describes the development of techniques used to model mixed-mode
crack propagation, in two-dimensions, by means of the finite element method.
These techniques are embodied in the FRacture ANalysis Code (FRANC).
Discrete crack propagation analysis using the finite element method is a very
complex problem. The use of the finite element method, however, is desirable
because it is currently the simplest way to analyze an arbitrary crack
configuration in an arbitrary structure subjected to arbitrary loading. Finite
element analysis is robust and is easily extended for nonlinear and dynamic
analysis. Finite element analysis of crack propagation is complex because of:
the large amount of information required for an analysis, the geometrical and
topological difficulties in creating a finite element mesh, the difficulties
in describing the problem to a computer, and the difficulties in extracting
and digesting the pertinent results.
It is shown that by integrating aspects of finite element analysis, fracture
mechanics, computer graphics, finite element postprocessing, automatic mesh
generation, and data structure design a powerful tool for fracture
investigations is created.
Fracture Mechanics Analysis of the Fontana Dam
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by
John Chappell
May, 1981
ABSTRACT
In 1972, a large crack was discovered on the downstream face of Fontana Dam. The crack was observed to intersect a drainage gallery and continue beyond the gallery for an unknown distance. A case study of Fontana Dam was performed to confirm the supposed crack mechanism, predict the approximate time of occurrence of initiation and predict the current extent and location of the crack.
This study is the first application of discrete crack modelling based on classic fracture mechanics concepts to an actual dam cracking problem.
A three-dimensional finite element analysis of the entire dam was first performed. This analysis confirmed that the crack mechanism was a combination of thermal expansion and thermally induced concrete growth. Theories of mixed-mode fracture propagation were then incorporated into a two dimensional finite element analysis to perform a fracture analysis on a cross-section of the cracked portion of the dam. The three-dimensional study generated displacements that were used as boundary conditions on the two-dimensional finite element mesh. The crack was allowed to initiate on the downstream face at the point it was observed; subsequent propagation was not dictated by original meshing, and the final mesh was substantially different from the initial mesh. Results indicated that the approximate time of occurrence of crack initiation was in the Fall, 1971. The two dimensional analysis also revealed that the interim measures undertaken by TVA to stabilize the cracked blocks did not influence the behavior of the dam. Finally, a lower bound prediction of the current crack front location was obtained.
Interactive and Graphic Two - Dimensional Fatigue Crack Propagation Analysis Using Boundary Element Method
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by Kodwo Otseidu
January, 1983
ABSTRACT
An automatic two-dimensional quasi-static and fatigue crack propagation analysis program using the boundary element method which has been proven accurate [1] was taken by the author and modified to have the following capabilities in Mode I fatigue analysis.
(a) Interactive fatigue analysis mode, with a data preprocessor
for generating the node coordinates on circular and straight
boundaries, element data, and nonzero boundary values.
(b) Graphic feedback during the initial elastic analysis,
alteration of crack direction, boundary modification and
node repositioning.
(c ) Alteration of crack increment length, the nominal stress
ratio, R. and the simulation of spectrum loads as a
series of constant amplitude loading.
(d) The incorporation of five fatigue crack growth models, four
of which are from the literature
proposed by the author.
The modified code, Boundary Element Fatigue Crack Propagation program (BEFCP), is used to predict the fatigue life of three example problems of 2024-T851 aluniniuml alloy. The problems studied are:
(a) The finite width and height plate with center crack under constant amplitude loading.
(b) The finite width and height plate with center crack under monotonically increasing spectrum load.
(c) The hole with an edge crack under constant amplitude edge
loading.
In the first two examples it was found that there was excellent agreement between the BEFCP analysis and the analytical results. This confirmed the correctness of the fatigue and spectrum load simulation algorithms adopted in the code.
In the third example the analysis did not show good agreement with both the finite element analysis and experimental measurements made by Zatz, et al. It was discovered that BEFCP cannot give good fatigue life prediction where growth retardation exists and where strict linear elastic fracture mechanics concepts do not apply.
An Experimental Investigation of Fatigue Cracking in Welded Crane Runway
Girders Due to Wheel Induced Stresses
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
Kirk I. Mettam
January, 1986
ABSTRACT
Extensive fatigue cracking in the welded details of crane runway girders occurs due to wheel induced stresses. The work reported in this thesis is an integral part of a project aimed at enhancing the capabilities of the designer in predicting the stresses in the welded details of concern. This work was performed through coordinated efforts in computer simulation and physical testing. The work reported herein is the result of the physical testing program. Static tests provided support of analytical efforts leading to proposed design solutions and an exploratory fatigue study was performed to evaluate fatigue crack propagation in a full penetration welded detail.
A thorough review of existing design solutions and the proposed Cornell solutions is presented. The Cornell
solutions have the attribute of including localized deformations of the rail and interaction effects between
investigated through the use of three dimensional finite element analyses and verified through physical testing.
A thorough report of the physical testing effort is given. Static tests, paralleled by three dimensional finite element analyses, aided in the development and refinement of the proposed design solutions and provided practical evaluations of analysis assumptions. One evaluation showed that the contact condition between the rail and the top of the girder has a pronounced influence on the stresses at the point of cracking. These important findings show that irregular contact conditions can increase the stresses in the welded details above those obtained in a uniform contact condition by as much as a factor of four. Tests showing the effect of uniform contact and elastomeric rail pads in reducing these peak stresses are also presented.
Various fatigue design approaches are discussed and a survey of recommendations for crane runway girders in various international design guidelines is presented. A review of the concepts of fracture mechanics is accompanied by a discussion of the issues involved in its application to fatigue cracking in crane runway girders. These are the effects of residual stress, crack closure, and failure definitions.
An exploratory fatigue test is reported in which crack propagation in the now recommended full penetration weld is reported. Such cracking has not yet been observed in service but is likely to appear as the more recently designed girders accummulate service life. Experimental
results are compared with predictions based on a series of three dimensional boundary element crack propagation analyses. An example of an inspection-based tool for fracture control is developed.
Lastly, the state of design practice in the U.S. is reviewed in light of the current project and suggestions for further study are presented.
Case Studies of Cracking of Concrete Dams - A Linear Elastic Approach
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by Wern Steve Lin
January, 1988
ABSTRACT
Linear elastic fracture mechanics was applied to simulate cracking of concrete dams. For the Fontana gravity dam, thermal loads were simulated by prescribing displacements to the boundary of the cracked crosssection. A two-dimensional fracture analysis was performed on the cross-section. The crack was simulated and compared with the site observation and a previous analysis. For the Kolnbrein arch dam, loadings were obtained by the trial-load method. The fracture analysis was performed on a twodimensional cantilever. Three cracks of Kolnbrein were simulated and comparisons with the real case were made. For the generic gravity dam, the crack propagated from the tip of a construction joint was simulated. Envelopes of critical joint lengths were made. Their derivation provides a reference of cracking control of concrete gravity dams. The dam factor-of-safety against sliding was calculated by both classical analysis and fracture analysis. The concordance between the two analysis suggests that fracture approach is a potential in evaluating the dam safety and its application to concrete dams is worth further study.
Two-Dimensional Numerical Evaluation of Near Wellbore Phenomena:
Perforation Performance & Interacting Hydraulic Fractures
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by Stephen James Lamkin
May, 1990
ABSTRACT
The thesis presents two-dimensional, finite element, evaluations of near wellbore phenomena, focusing on the performance of perforations and the interaction of hydraulic fractures. Stress, poroelastic and fracture propagation studies have been conducted to begin evaluating near wellbore phenomena. In addition, these studies are serving to calibrate computational mechanics tools and to develop a knowledge base from which three-dimensional simulations can be furthered.
The first four chapters of the thesis introduce the ongoing, cooperative, research project and aspects of the disciplines involved in this interdisciplinary research environment (for example, reservoir stimulation, fracture mechanics and poroelasticity). In addition, a review of research addressing aspects of the project such as perforation performance and factors influencing the growth of hydraulic fractures is presented. Models and results are presented which consider stress analyses of borehole-perforation(s) configurations, poroelastic evaluations of a perforation, and interaction of hydraulic fractures emanating from adjacent perforations. The results raise many issues addressing the design, orientation and function of perforations, and provide insights into the near wellbore interaction of hydraulic fractures.
The thesis demonstrates that the orientation, geometry and integrity of the perforations (for example, plugging) can significantly affect the local stress field, breakdown pressure, perforation functionality and possible location of fracture initiation.
For example. results indicate that, within the assumptions of two
dimensional analysis. an optimal orientation of the perforation with
respect to in-situ stresses does exist which, if exploited, could
reduce fracture initiation pressures. In addition, the perforation
might collapse if it is not designed, executed and cleaned properly.
Also, the perforation and its length can be rendered ineffective due
to plugging or the formation of a micro-annulus due to a poor
cement job. In either case, crack initiation would ignore the
perforation length entirely.
Results from the study of collinear and near collinear interacting
fractures suggest that crack tip interaction can affect the fracture
geometry. As a consequence, an increased pressurization rate
might be required in order to maintain the same fracture fluid
pressure. Furthermore, the nature of the interaction could
adversely influence proppant transport. In addition, crack tip
interaction influences the corresponding Mode I stress intensity
such that an initially collinear array of cracks would interact and
coalesce non-uniformly. Also, an initial offset between the
interacting cracks does not affect the character of the interaction.
Finally, the correlation between the numerical results presented
in the thesis and experimental, analytical, and numerical results
generated by others has served to build confidence in the accuracy
and utility of the computational mechanics tools used.
Fracture Analysis Code: A Computer - Aided Teaching Tool
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by Maya Srinivasan
January 1988
ABSTRACT
This thesis describes the creation of an effective computer-aided teaching tool for courses in the finite element method and fracture mechanics. The tool was developed by modifying and enhancing an exisiting program, the FRacture ANalysis Code, FRANC.
FRANC was originally developed to model two-dimensional, linear, elastic fracture processes. It used the finite element method to perform analysis and functioned in an interactive, graphics environment. It was developed on Digital Equipment Corporation's Vaxstation II/GPX and used the resident system graphics. FRANC's element library was limited to quadratic elements. To make FRANC a general-purpose finite element and fracture-mechanics package, new elements were added to the library. The program was made portable by implementing it on a commercially available, device-independent, graphics system, HOOPS. The user-interface was re-structured to be more friendly robust, and instructive. A complete documentation of the package, including a tutorial and a library of example problems, was compiled.
This instructional program was developed as a part of Project SOCRATES, a program at Cornell University instituted by the U.S. Department of Education's FIPSE.
Decohesion of Grain Boundaries in Statistical Representations of Aluminum Polycrystals.
A Thesis
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
by Erin Iesulauro
January 2002
ABSTRACT
Fatigue cracks have long been a cause of failure of aluminum alloy components in
aerospace applications. Extensive work has been done to study the rate at which fatigue cracks will propagate in order to determine the fatigue life of a system. However, much of the fatigue life actually resides in the initiation and small crack growth phases of fatigue crack life. To investigate fatigue crack initiation a multiscale modeling approach has been taken to capture the heterogeneous nature of the microstructure and its influence on when and where fatigue cracks will initiate. Material samples were created at the polycrystal scale so that individual grains were discretized in the model. Grain boundaries were modeled using coupled cohesive zone models. Finite element analyses were then conducted under monotonic and cyclic loading. A parametric study was conducted loading statistical polycrystal samples under monotonic loading. Samples were tested varying geometries, grain material models and properties, and grain boundary properties. Results showed the greatest sensitivities to material parameter values when using orthotropic material models and to the relative values of grain yield stress and grain boundary strength. An elastic-plastic sample was also cyclically loaded. Observations showed increasing damage with each cycle. Final localized failure of several grain boundaries is shown after several cycles. The simulation tools created result in a useful tool for continued studied of grain boundary failure that may lead to initiation of a fatigue crack.
Simulations of Crack Initiation in Aluminium Alloys with Inclusions
A Thesis Presented to the Faculty of the Graduate
School of Cornell University in Partial Fulfillment of the Requirements for the
Degree of Master of Science
by Ketan Manek Dodhia January 2002
ABSTRACT
Some preliminary work is made in the study of the impact of inclusions particles
on fatigue crack initiation in aluminum alloys, through numerical simulation.
The work is divided into two parts.
In the first part, a framework is developed for generating representative
microstructure models. Particular attention is given to producing models that
phenomenologically depict real aluminum microstructure topologies. Statistical
methods are employed to achieve this, and the framework allows for the creation
of an arbitrary large number of microstructure models.
In the second part, the microstructure models are analyzed with finite element
analysis. Since it has been observed that inclusion particles provide
preferential sites for crack nucleation, and the method of nucleation is often
by debonding of the particle from the surrounding matrix or grain, cohesive zone
interface material models were utilized to simulate this process at the
particles. The result is a simulation where cracks are not introduced
explicitly, but rather allowed to nucleate naturally as particles decohere from
the grains.
Ferguson
Spievak
Polaha
Ural
