Foundation failure modes and field symptoms

Foundation failure modes and field symptoms

Differential Settlement

Differential settlement is a common and significant failure mode in foundation engineering, referring to the uneven settling of a structures foundation. This phenomenon occurs when different parts of the foundation settle at different rates or to different extents, leading to structural distortions and potential damage. Understanding differential settlement is crucial for engineers and architects to ensure the longevity and safety of buildings.


The primary cause of differential settlement is the variation in soil properties beneath the foundation. Micropiles serve tight access or heavy load situations home foundation repair services differential settlement.. Soils can vary in composition, density, moisture content, and load-bearing capacity. When a foundation is constructed over such varying soil conditions, some parts may settle more than others. This uneven settling can be exacerbated by factors such as poor soil compaction, inadequate foundation design, or external loads that are not evenly distributed.


Field symptoms of differential settlement are often visible and can include cracks in walls, floors, and ceilings, misaligned doors and windows, and uneven floors. These symptoms not only affect the aesthetic appeal of a structure but can also compromise its structural integrity. In severe cases, differential settlement can lead to significant structural damage, requiring costly repairs or even necessitating the demolition and reconstruction of the affected areas.


To mitigate the risks associated with differential settlement, engineers employ various strategies during the design and construction phases. These include conducting thorough soil investigations to understand the underlying soil conditions, designing foundations that can accommodate varying settlement, and using techniques such as soil stabilization or deep foundations to ensure uniform support. Regular monitoring of the structure post-construction can also help in early detection and management of differential settlement issues.


In conclusion, differential settlement is a critical consideration in foundation engineering. By understanding its causes, recognizing its symptoms, and implementing appropriate design and construction practices, engineers can significantly reduce the risk of this failure mode, ensuring the stability and safety of structures over time.

Certainly! When discussing the failure modes and field symptoms of foundations, two critical phenomena to consider are heaving and uplift. These terms, though often used in engineering contexts, can be understood with a bit of explanation.


Heaving refers to the upward movement of the ground or soil beneath a foundation. This can occur due to several reasons, most commonly the expansion of soil when it absorbs water. Clay soils are particularly notorious for this behavior. When clay gets wet, it swells, pushing the foundation upwards. This can lead to significant structural issues, including cracks in walls, misaligned doors and windows, and even the tilting of the building. Heaving is a gradual process, often exacerbated by seasonal changes or poor drainage around the building.


Uplift, on the other hand, is a more direct and often more dramatic form of foundation failure. It occurs when the foundation is literally lifted off the ground. This can happen due to extreme weather conditions, such as high winds or flooding, which exert upward pressure on the foundation. Another common cause is the expansion of soil beneath the foundation, similar to heaving, but uplift implies a more pronounced and often sudden movement. Uplift can lead to severe structural damage, including the detachment of the foundation from the ground, which can compromise the entire buildings stability.


In the field, identifying symptoms of heaving and uplift is crucial for early intervention. Signs of heaving might include uneven floors, cracks in the foundation or walls that are wider at the top than at the bottom, and doors and windows that stick or dont close properly. Uplift symptoms might be more dramatic, such as visible gaps between the foundation and the ground, significant cracks in the foundation, and in severe cases, the building might appear to be tilting or lifting off the ground.


Understanding these failure modes is essential for engineers and homeowners alike. Regular inspections, proper drainage systems, and choosing the right type of foundation for the soil conditions can help mitigate the risks associated with heaving and uplift. In cases where these issues are already present, professional assessment and repair are crucial to ensure the safety and longevity of the structure.

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Seasonal drought patterns drive more basement wall problems in Hoffman Estates

Seasonal drought patterns drive more basement wall problems in Hoffman Estates

In recent years, Hoffman Estates has faced increasing challenges due to seasonal drought patterns, which have significantly contributed to more basement wall problems.. As we look towards the future, it is crucial to consider both the projections of these drought patterns and the adaptation strategies that can be implemented to mitigate their impact. Future projections indicate that climate change will likely exacerbate the frequency and severity of droughts in the region.

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United Structural Systems of Illinois tracks rising cases of stair step brick cracks

United Structural Systems of Illinois tracks rising cases of stair step brick cracks

In recent years, the United Structural Systems of Illinois has been closely monitoring a concerning trend: the rising incidence of stair step brick cracks in residential and commercial buildings.. This phenomenon, characterized by diagonal cracks that resemble the steps of a staircase, poses significant structural and aesthetic challenges.

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Tree root growth tied to foundation movement in Cook County neighborhoods

Tree root growth tied to foundation movement in Cook County neighborhoods

Certainly!. Heres a human-like, conversational essay on Mitigation Strategies for Homeowners and Local Authorities regarding Tree Root Growth and Foundation Movement in Cook County neighborhoods: In Cook County, like many other places, the relationship between tree root growth and foundation movement is a topic that homeowners and local authorities need to pay close attention to.

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Cracking and Spalling

Certainly! When discussing foundation failure modes and their field symptoms, two common issues that often arise are cracking and spalling. These problems can indicate underlying issues with the foundation that, if left unaddressed, may lead to more severe structural problems.


Cracking is a prevalent symptom of foundation distress. It occurs when the foundation material, whether its concrete, brick, or stone, experiences stress beyond its capacity. This stress can be due to a variety of factors such as soil movement, poor construction practices, or the natural settling of the structure over time. Cracks can vary in size and severity; some may be hairline fractures that are barely noticeable, while others can be wide and deep, indicating significant movement or settlement. Its important to note that not all cracks are cause for alarm; minor cracking can occur as the foundation settles, especially in new constructions. However, cracks that are wider than a quarter-inch, are increasing in size, or are accompanied by other symptoms like doors and windows sticking, should be evaluated by a professional to determine the cause and appropriate course of action.


Spalling, on the other hand, is a more specific type of damage that affects concrete foundations. It occurs when pieces of the concrete surface begin to break off or flake away. This is often a result of the reinforcement within the concrete, such as steel rebar, corroding and expanding. As the steel corrodes, it creates pressure that causes the concrete to crack and eventually spall. Spalling can also be caused by freeze-thaw cycles in colder climates, where water penetrates the concrete, freezes, expands, and causes the surface to break apart. Like cracking, spalling is a sign that the foundation is under stress and may be experiencing more significant issues beneath the surface.


Both cracking and spalling are serious symptoms that should not be ignored. They can lead to water infiltration, which can further weaken the foundation and compromise the structural integrity of the entire building. Addressing these issues typically involves repairing the damaged areas, ensuring proper drainage around the foundation, and sometimes installing additional support systems like piers or helical anchors to stabilize the structure.


In conclusion, cracking and spalling are critical indicators of potential foundation failure. Homeowners and property managers should be vigilant in monitoring their foundations for these signs and seek professional advice when necessary to prevent more extensive and costly damage in the future.

Cracking and Spalling

Corrosion and Deterioration

Sure, heres a short essay on the topic of corrosion and deterioration as failure modes in foundations, along with their field symptoms:




Corrosion and deterioration are critical failure modes that can significantly impact the integrity and longevity of foundations. Understanding these processes and recognizing their symptoms in the field is essential for maintaining structural safety and preventing catastrophic failures.


Corrosion primarily affects metallic components within or attached to foundations, such as reinforcing steel in concrete. When exposed to moisture and oxygen, steel undergoes a chemical reaction that converts it into rust. This process not only weakens the metal but also causes it to expand, leading to cracks in the surrounding concrete. Field symptoms of corrosion include visible rust stains on the surface of the concrete, spalling (chipping away) of the concrete cover, and bulging or distortion of the structural elements. In severe cases, corrosion can compromise the bond between the steel and the concrete, reducing the overall load-bearing capacity of the foundation.


Deterioration, on the other hand, encompasses a broader range of processes that degrade the material properties of the foundation. This can include chemical attacks from sulfates or acids in the soil, freeze-thaw cycles in colder climates, and biological activity such as root intrusion. Deterioration symptoms vary depending on the specific cause but often manifest as cracking, erosion of material, efflorescence (white crystalline deposits on the surface), and a general decline in the structural integrity of the foundation. For instance, sulfate attack can lead to expansion and cracking of concrete, while freeze-thaw cycles can cause spalling and surface scaling.


In the field, identifying these symptoms early is crucial for implementing timely repairs and preventing further damage. Regular inspections should look for signs of moisture ingress, unusual cracking patterns, and any visible signs of material degradation. Addressing the root causes of corrosion and deterioration, such as improving drainage around the foundation, applying protective coatings, or replacing damaged sections, can help extend the lifespan of the structure and ensure its continued safety and functionality.


In conclusion, corrosion and deterioration are significant concerns for foundation integrity. By understanding these failure modes and their associated field symptoms, engineers and property owners can take proactive measures to maintain and protect their structures, ensuring long-term durability and safety.

Building and construction is the process associated with supplying buildings, infrastructure, industrial centers, and associated tasks via to the end of their life. It normally begins with preparation, financing, and style that proceeds till the property is built and on-line. Construction likewise covers fixings and upkeep job, any type of jobs to expand, expand and improve the asset, and its ultimate demolition, taking down or deactivating. The construction sector contributes significantly to several countries' gdps (GDP). International expense on building and construction activities had to do with $4 trillion in 2012. In 2022, expense on the building market went beyond $11 trillion a year, equal to around 13 percent of international GDP. This investing was forecasted to climb to around $14. 8 trillion in 2030. The building and construction industry promotes economic advancement and brings lots of non-monetary advantages to numerous nations, however it is among one of the most hazardous industries. For example, regarding 20% (1,061) of US industry deaths in 2019 occurred in construction.

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Ductile failure of a metallic specimen strained axially

Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band, or dislocation.[1]

Brittle fractures occur without any apparent deformation before fracture. Ductile fractures occur after visible deformation. Fracture strength, or breaking strength, is the stress when a specimen fails or fractures. The detailed understanding of how a fracture occurs and develops in materials is the object of fracture mechanics.

Strength

[edit]
Stress vs. strain curve typical of aluminum
  1. Ultimate tensile strength
  2. Yield strength
  3. Proportional limit stress
  4. Fracture
  5. Offset strain (typically 0.2%)

Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture.[2] This is usually determined for a given specimen by a tensile test, which charts the stress–strain curve (see image). The final recorded point is the fracture strength.

Ductile materials have a fracture strength lower than the ultimate tensile strength (UTS), whereas in brittle materials the fracture strength is equivalent to the UTS.[2] If a ductile material reaches its ultimate tensile strength in a load-controlled situation,[Note 1] it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled,[Note 2] the deformation of the material may relieve the load, preventing rupture.

The statistics of fracture in random materials have very intriguing behavior, and was noted by the architects and engineers quite early. Indeed, fracture or breakdown studies might be the oldest physical science studies, which still remain intriguing and very much alive. Leonardo da Vinci, more than 500 years ago, observed that the tensile strengths of nominally identical specimens of iron wire decrease with increasing length of the wires (see e.g.,[3] for a recent discussion). Similar observations were made by Galileo Galilei more than 400 years ago. This is the manifestation of the extreme statistics of failure (bigger sample volume can have larger defects due to cumulative fluctuations where failures nucleate and induce lower strength of the sample).[4]

Types

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There are two types of fractures: brittle and ductile fractures respectively without or with plastic deformation prior to failure.

Brittle

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Brittle fracture in glass
A roughly ovoid metal cylinder, viewed end-on. The bottom-right portion of the metal's end surface is dark and slightly disfigured, whereas the rest is a much lighter colour and not disfigured.
Fracture of an aluminum crank arm of a bicycle, where the bright areas display a brittle fracture, and the dark areas show fatigue fracture

In brittle fracture, no apparent plastic deformation takes place before fracture. Brittle fracture typically involves little energy absorption and occurs at high speeds—up to 2,133.6 m/s (7,000 ft/s) in steel.[5] In most cases brittle fracture will continue even when loading is discontinued.[6]

In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension.

The fracture strength (or micro-crack nucleation stress) of a material was first theoretically estimated by Alan Arnold Griffith in 1921:

where: –

Brittle cleavage fracture surface from a scanning electron microscope
is the Young's modulus of the material,
is the surface energy, and
is the micro-crack length (or equilibrium distance between atomic centers in a crystalline solid).

On the other hand, a crack introduces a stress concentration modeled by Inglis's equation[7]

(For sharp cracks)

where:

is the loading stress,
is half the length of the crack, and
is the radius of curvature at the crack tip.

Putting these two equations together gets

Sharp cracks (small ) and large defects (large ) both lower the fracture strength of the material.

Recently, scientists have discovered supersonic fracture, the phenomenon of crack propagation faster than the speed of sound in a material.[8] This phenomenon was recently also verified by experiment of fracture in rubber-like materials.

The basic sequence in a typical brittle fracture is: introduction of a flaw either before or after the material is put in service, slow and stable crack propagation under recurring loading, and sudden rapid failure when the crack reaches critical crack length based on the conditions defined by fracture mechanics.[6] Brittle fracture may be avoided by controlling three primary factors: material fracture toughness (Kc), nominal stress level (σ), and introduced flaw size (a).[5] Residual stresses, temperature, loading rate, and stress concentrations also contribute to brittle fracture by influencing the three primary factors.[5]

Under certain conditions, ductile materials can exhibit brittle behavior. Rapid loading, low temperature, and triaxial stress constraint conditions may cause ductile materials to fail without prior deformation.[5]

Ductile

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Schematic representation of the steps in ductile fracture (in pure tension)

In ductile fracture, extensive plastic deformation (necking) takes place before fracture. The terms "rupture" and "ductile rupture" describe the ultimate failure of ductile materials loaded in tension. The extensive plasticity causes the crack to propagate slowly due to the absorption of a large amount of energy before fracture.[9][10]

Ductile fracture surface of 6061-T6 aluminum

Because ductile rupture involves a high degree of plastic deformation, the fracture behavior of a propagating crack as modelled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation ahead of the crack as it propagates.

The basic steps in ductile fracture are microvoid[11] formation, microvoid coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface. The microvoids nucleate at various internal discontinuities, such as precipitates, secondary phases, inclusions, and grain boundaries in the material.[11] As local stress increases the microvoids grow, coalesce and eventually form a continuous fracture surface.[11] Ductile fracture is typically transgranular and deformation due to dislocation slip can cause the shear lip characteristic of cup and cone fracture.[12]

The microvoid coalescence results in a dimpled appearance on the fracture surface. The dimple shape is heavily influenced by the type of loading. Fracture under local uniaxial tensile loading usually results in formation of equiaxed dimples. Failures caused by shear will produce elongated or parabolic shaped dimples that point in opposite directions on the matching fracture surfaces. Finally, tensile tearing produces elongated dimples that point in the same direction on matching fracture surfaces.[11]

Characteristics

[edit]

The manner in which a crack propagates through a material gives insight into the mode of fracture. With ductile fracture a crack moves slowly and is accompanied by a large amount of plastic deformation around the crack tip. A ductile crack will usually not propagate unless an increased stress is applied and generally cease propagating when loading is removed.[6] In a ductile material, a crack may progress to a section of the material where stresses are slightly lower and stop due to the blunting effect of plastic deformations at the crack tip. On the other hand, with brittle fracture, cracks spread very rapidly with little or no plastic deformation. The cracks that propagate in a brittle material will continue to grow once initiated.

Crack propagation is also categorized by the crack characteristics at the microscopic level. A crack that passes through the grains within the material is undergoing transgranular fracture. A crack that propagates along the grain boundaries is termed an intergranular fracture. Typically, the bonds between material grains are stronger at room temperature than the material itself, so transgranular fracture is more likely to occur. When temperatures increase enough to weaken the grain bonds, intergranular fracture is the more common fracture mode.[6]

Testing

[edit]

Fracture in materials is studied and quantified in multiple ways. Fracture is largely determined by the fracture toughness (), so fracture testing is often done to determine this. The two most widely used techniques for determining fracture toughness are the three-point flexural test and the compact tension test.

By performing the compact tension and three-point flexural tests, one is able to determine the fracture toughness through the following equation:

Where:

is an empirically-derived equation to capture the test sample geometry
is the fracture stress, and
is the crack length.

To accurately attain , the value of must be precisely measured. This is done by taking the test piece with its fabricated notch of length and sharpening this notch to better emulate a crack tip found in real-world materials.[13] Cyclical prestressing the sample can then induce a fatigue crack which extends the crack from the fabricated notch length of to . This value is used in the above equations for determining .[14]

Following this test, the sample can then be reoriented such that further loading of a load (F) will extend this crack and thus a load versus sample deflection curve can be obtained. With this curve, the slope of the linear portion, which is the inverse of the compliance of the material, can be obtained. This is then used to derive f(c/a) as defined above in the equation. With the knowledge of all these variables, can then be calculated.

Ceramics and inorganic glasses

[edit]

Ceramics and inorganic glasses have fracturing behavior that differ those of metallic materials. Ceramics have high strengths and perform well in high temperatures due to the material strength being independent of temperature. Ceramics have low toughness as determined by testing under a tensile load; often, ceramics have values that are ~5% of that found in metals.[14] However, as demonstrated by Faber and Evans, fracture toughness can be predicted and improved with crack deflection around second phase particles.[15] Ceramics are usually loaded in compression in everyday use, so the compressive strength is often referred to as the strength; this strength can often exceed that of most metals. However, ceramics are brittle and thus most work done revolves around preventing brittle fracture. Due to how ceramics are manufactured and processed, there are often preexisting defects in the material introduce a high degree of variability in the Mode I brittle fracture.[14] Thus, there is a probabilistic nature to be accounted for in the design of ceramics. The Weibull distribution predicts the survival probability of a fraction of samples with a certain volume that survive a tensile stress sigma, and is often used to better assess the success of a ceramic in avoiding fracture.

Fiber bundles

[edit]

To model fracture of a bundle of fibers, the Fiber Bundle Model was introduced by Thomas Pierce in 1926 as a model to understand the strength of composite materials.[16] The bundle consists of a large number of parallel Hookean springs of identical length and each having identical spring constants. They have however different breaking stresses. All these springs are suspended from a rigid horizontal platform. The load is attached to a horizontal platform, connected to the lower ends of the springs. When this lower platform is absolutely rigid, the load at any point of time is shared equally (irrespective of how many fibers or springs have broken and where) by all the surviving fibers. This mode of load-sharing is called Equal-Load-Sharing mode. The lower platform can also be assumed to have finite rigidity, so that local deformation of the platform occurs wherever springs fail and the surviving neighbor fibers have to share a larger fraction of that transferred from the failed fiber. The extreme case is that of local load-sharing model, where load of the failed spring or fiber is shared (usually equally) by the surviving nearest neighbor fibers.[4]

Disasters

[edit]

Failures caused by brittle fracture have not been limited to any particular category of engineered structure.[5] Though brittle fracture is less common than other types of failure, the impacts to life and property can be more severe.[5] The following notable historic failures were attributed to brittle fracture:

Computational fracture mechanics

[edit]

Virtually every area of engineering has been significantly impacted by computers, and fracture mechanics is no exception. Since there are so few actual problems with closed-form analytical solutions, numerical modelling has become an essential tool in fracture analysis. There are literally hundreds of configurations for which stress-intensity solutions have been published, the majority of which were derived from numerical models. The J integral and crack-tip-opening displacement (CTOD) calculations are two more increasingly popular elastic-plastic studies. Additionally, experts are using cutting-edge computational tools to study unique issues such as ductile crack propagation, dynamic fracture, and fracture at interfaces. The exponential rise in computational fracture mechanics applications is essentially the result of quick developments in computer technology.[17]

Most used computational numerical methods are finite element and boundary integral equation methods. Other methods include stress and displacement matching, element crack advance in which latter two come under Traditional Methods in Computational Fracture Mechanics.

Fine Mesh done in Rectangular area in Ansys software (Finite Element Method)

The finite element method

[edit]

The structures are divided into discrete elements of 1-D beam, 2-D plane stress or plane strain, 3-D bricks or tetrahedron types. The continuity of the elements are enforced using the nodes.[17]

The boundary integral equation method

[edit]

In this method, the surface is divided into two regions: a region where displacements are specified Su and region with tractions are specified ST . With given boundary conditions, the stresses, strains, and displacements within the body can all theoretically be solved for, along with the tractions on Su and the displacements on ST. It is a very powerful technique to find the unknown tractions and displacements.[17]

Traditional methods in computational fracture mechanics

[edit]

These methods are used to determine the fracture mechanics parameters using numerical analysis.[17] Some of the traditional methods in computational fracture mechanics, which were commonly used in the past, have been replaced by newer and more advanced techniques. The newer techniques are considered to be more accurate and efficient, meaning they can provide more precise results and do so more quickly than the older methods. Not all traditional methods have been completely replaced, as they can still be useful in certain scenarios, but they may not be the most optimal choice for all applications.

Some of the traditional methods in computational fracture mechanics are:

  • Stress and displacement matching
  • Elemental crack advance
  • Contour integration
  • Virtual crack extension

See also

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Notes

[edit]
  1. ^ A simple load-controlled tensile situation would be to support a specimen from above, and hang a weight from the bottom end. The load on the specimen is then independent of its deformation.
  2. ^ A simple displacement-controlled tensile situation would be to attach a very stiff jack to the ends of a specimen. As the jack extends, it controls the displacement of the specimen; the load on the specimen is dependent on the deformation.

References

[edit]
  1. ^ Cherepanov, G.P., Mechanics of Brittle Fracture
  2. ^ a b Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003), Materials and Processes in Manufacturing (9th ed.), Wiley, p. 32, ISBN 0-471-65653-4.
  3. ^ Lund, J. R.; Bryne, J. P., Civil. Eng. and Env. Syst. 18 (2000) 243
  4. ^ a b Chakrabarti, Bikas K. (December 2017). "Story of the Developments in Statistical Physics of Fracture, Breakdown and Earthquake: A Personal Account". Reports in Advances of Physical Sciences. 01 (4): 1750013. doi:10.1142/S242494241750013X. ISSN 2424-9424. Text was copied from this source, which is available under a Creative Commons Attribution 4.0 International License.
  5. ^ a b c d e f g h i Rolfe, John M. Barsom, Stanley T. (1999). Fracture and fatigue control in structures: applications of fracture mechanics (3 ed.). West Conshohocken, Pa.: ASTM. ISBN 0-8031-2082-6.cite book: CS1 maint: multiple names: authors list (link)
  6. ^ a b c d e f g Campbell, F.C., ed. (2012). Fatigue and fracture: understanding the basics. Materials Park, Ohio: ASM International. ISBN 978-1-61503-976-0.
  7. ^ Inglis, Charles E. (1913). "Stresses in a plate due to the presence of cracks and sharp corners" (PDF). Transactions of the Institution of Naval Architects. 55: 219–230.
  8. ^ C. H. Chen; H. P. Zhang; J. Niemczura; K. Ravi-Chandar; M. Marder (November 2011). "Scaling of crack propagation in rubber sheets". Europhysics Letters. 96 (3) 36009. Bibcode:2011EL.....9636009C. doi:10.1209/0295-5075/96/36009. S2CID 5975098.
  9. ^ Perez, Nestor (2016). Fracture Mechanics (2nd ed.). Springer. ISBN 978-3-319-24997-1.
  10. ^ Callister, William D. Jr. (2018). Materials science and engineering: an introduction (8th ed.). Wiley. pp. 236–237. ISBN 978-1-119-40539-9. OCLC 992798630.
  11. ^ a b c d Ewalds, H. L. (1985). Fracture mechanics. R. J. H. Wanhill. London: E. Arnold. ISBN 0-7131-3515-8. OCLC 14377078.
  12. ^ Askeland, Donald R.; Wright, Wendelin J. (January 2015). The science and engineering of materials (Seventh ed.). Boston, MA. pp. 236–237. ISBN 978-1-305-07676-1. OCLC 903959750.cite book: CS1 maint: location missing publisher (link)
  13. ^ An improved semi-analytical solution for stress at round-tip notches, a closer look
  14. ^ a b c Courtney, Thomas H. (2000), Mechanical behavior of materials (3nd ed.), McGraw Hill, ISBN 1-57766-425-6.
  15. ^ Faber, K. T.; Evans, A. G. (1 April 1983). "Crack deflection processes—I. Theory". Acta Metallurgica. 31 (4): 565–576. doi:10.1016/0001-6160(83)90046-9. ISSN 0001-6160.
  16. ^ Pierce, F. T., J. Textile Indust. 17 (1926) 355
  17. ^ a b c d Anderson, T. L. (2005). Fracture mechanics: fundamentals and applications (3rd ed.). Boca Raton, FL. ISBN 978-1-4200-5821-5. OCLC 908077872.cite book: CS1 maint: location missing publisher (link)

Further reading

[edit]
  • Dieter, G. E. (1988) Mechanical Metallurgy ISBN 0-07-100406-8
  • A. Garcimartin, A. Guarino, L. Bellon and S. Cilberto (1997) "Statistical Properties of Fracture Precursors". Physical Review Letters, 79, 3202 (1997)
  • Callister Jr., William D. (2002) Materials Science and Engineering: An Introduction. ISBN 0-471-13576-3
  • Peter Rhys Lewis, Colin Gagg, Ken Reynolds, CRC Press (2004), Forensic Materials Engineering: Case Studies.
[edit]

 

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