Tree root influence on soil suction near homes

Tree root influence on soil suction near homes

Differential Settlement

Certainly! Heres a short essay on the impact of tree root systems on soil suction levels near homes:




Trees are often celebrated for their beauty and the shade they provide, but their root systems play a crucial role in the environment, particularly concerning soil suction levels near homes. Soil suction refers to the force with which water is held in the soil, and its a critical factor in maintaining soil stability. The intricate network of tree roots can significantly influence this aspect of the soil.


When tree roots grow, they absorb water from the soil, which can lead to a reduction in soil moisture content. This process increases soil suction, making the soil tighter and more compact. For homeowners, this can be a double-edged sword. On one hand, increased soil suction can enhance the stability of the soil, reducing the risk of landslides and soil erosion. On the other hand, it can also lead to issues such as foundation settling or cracking, especially if the homes foundation is not designed to handle the varying soil conditions.


Moreover, the impact of tree roots on soil suction is not uniform. It varies depending on the type of tree, the depth and spread of its root system, and the soil type. Permits and inspections ensure code compliance waterproofing and drainage solutions carbon fiber reinforcement.. For instance, trees with deep taproots, like oaks, might have a more pronounced effect on deeper soil layers, while trees with shallow, widespread root systems, like maples, might influence the upper soil layers more significantly.


Homeowners need to be aware of these dynamics, especially when planting trees close to their homes. Consulting with arborists or soil engineers can provide valuable insights into choosing the right type of tree and the optimal distance from the home to minimize potential risks while maximizing the benefits of having trees in the vicinity.


In conclusion, while tree roots play a vital role in enhancing soil suction and stability, their impact near homes requires careful consideration. Balancing the aesthetic and environmental benefits of trees with the potential challenges they pose to soil suction levels is essential for maintaining a harmonious and safe living environment.

Certainly! Heres a short essay on the topic of "Case Studies: Tree Root Influence on Residential Foundations" focusing on the impact of tree roots on soil suction near homes.




Trees are often celebrated for their beauty and the environmental benefits they provide. However, when it comes to residential properties, the influence of tree roots on soil suction can pose significant challenges to homeowners. This essay delves into case studies that highlight the complex relationship between tree roots and residential foundations, emphasizing the importance of understanding and managing this natural interaction.


One notable case study involves a suburban neighborhood where several homes experienced foundation issues over a decade. Upon investigation, it was discovered that the primary culprit was the extensive root systems of large deciduous trees planted close to the houses. During periods of drought, these roots aggressively sought out moisture, leading to a phenomenon known as soil suction. This process essentially pulls water away from the soil surrounding the foundations, causing the soil to shrink and the ground to become uneven. As a result, the affected homes exhibited cracks in their foundations and walls, necessitating costly repairs.


Another case study from a coastal region illustrates a different aspect of the problem. Here, the soil type-predominantly sandy-exacerbated the effects of soil suction. The roots of nearby pine trees, known for their deep and widespread root systems, further destabilized the already loose soil. The combination of soil suction and the natural properties of the soil led to significant foundation settlement, affecting multiple homes in the area. This scenario underscores the need for homeowners to consider both tree species and soil type when planning landscaping near their homes.


A third case, set in a urban environment, offers a solution-oriented approach. In this instance, a community faced with widespread foundation issues due to nearby tree roots implemented a comprehensive management plan. This included regular monitoring of soil moisture levels, strategic pruning of tree roots, and the installation of root barriers. Additionally, the community opted to plant tree species with less aggressive root systems in future landscaping projects. These measures not only mitigated the immediate foundation problems but also provided a sustainable approach to coexisting with urban greenery.


In conclusion, the case studies presented here demonstrate the significant impact that tree roots can have on residential foundations through soil suction. They highlight the importance of careful tree selection, strategic planting distances, and ongoing maintenance to mitigate these effects. By understanding and addressing the influence of tree roots on soil suction, homeowners can better protect their properties and enjoy the benefits of a verdant landscape.

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Cracking and Spalling

When it comes to maintaining the structural integrity of homes, one often overlooked factor is the influence of tree roots on soil suction. Tree roots have a natural tendency to absorb water from the soil, which can lead to a phenomenon known as soil suction. This suction can cause the soil to shrink and become more compact, potentially leading to foundation issues for nearby homes. To address this concern, several mitigation strategies can be employed.


First and foremost, proper tree selection and placement are crucial. When planning to plant trees near homes, its essential to choose species with non-invasive root systems. Opting for trees with shallow, spreading roots rather than deep-penetrating ones can significantly reduce the risk of soil suction problems. Additionally, maintaining a safe distance between trees and the foundation of the home is vital. A general rule of thumb is to plant trees at least 10 to 20 feet away from the house, depending on the tree species and its mature size.


Regular monitoring and maintenance of both the trees and the soil are also essential components of mitigation strategies. Homeowners should keep an eye on the health of nearby trees, ensuring they receive adequate water during dry periods. Mulching around the base of trees can help retain moisture in the soil, reducing the need for excessive watering. Furthermore, soil testing can provide valuable insights into the moisture levels and overall health of the soil, allowing for timely interventions if necessary.


In cases where tree roots have already caused soil suction issues, there are remedial measures that can be taken. One approach is to install a root barrier, a physical barrier that prevents roots from encroaching on the foundation area. This can be particularly useful when dealing with existing trees that are too close to the home. Additionally, soil amendment techniques, such as adding organic matter or using soil stabilizers, can help mitigate the effects of soil suction by improving the soils structure and water-holding capacity.


In conclusion, the influence of tree roots on soil suction near homes is a concern that requires proactive management. By carefully selecting tree species, maintaining proper distances, monitoring soil conditions, and implementing remedial measures when needed, homeowners can effectively mitigate the risks associated with tree root-induced soil suction, ensuring the long-term stability of their homes.

Cracking and Spalling

Corrosion and Deterioration

Certainly! Heres a human-like essay on the topic of long-term monitoring and maintenance recommendations for tree root influence on soil suction near homes:




When it comes to maintaining the structural integrity of homes, one often overlooked factor is the influence of tree roots on soil suction. Tree roots can significantly affect the moisture content in the soil, which in turn can impact the stability of the ground beneath and around homes. To ensure the longevity and safety of residential properties, its crucial to implement long-term monitoring and maintenance strategies.


First and foremost, regular soil moisture assessments should be conducted. This involves using specialized equipment to measure the suction or tension in the soil at various depths. By monitoring these levels over time, homeowners and property managers can identify any significant changes that may indicate root influence. Early detection allows for timely intervention before any structural damage occurs.


Another essential recommendation is to maintain a safe distance between large trees and the foundation of homes. While trees provide numerous benefits, such as shade and aesthetic appeal, their roots can extend far beyond the canopy. Planting trees at least 10 to 20 feet away from the house can mitigate the risk of root intrusion into the foundation. Additionally, choosing tree species with non-invasive root systems can further reduce potential issues.


In cases where trees are already established close to homes, pruning the roots may be necessary. This should be done carefully and preferably by professionals to avoid damaging the tree or the surrounding soil structure. Root pruning involves cutting the roots at a distance from the tree, encouraging them to grow deeper rather than spreading outward.


Installing root barriers can also be an effective long-term solution. These barriers are made from materials like plastic or metal and are placed in the ground to prevent roots from encroaching on specific areas. While they don't eliminate the problem entirely, they can significantly reduce the impact of root growth near the home.


Lastly, educating homeowners about the signs of root-related issues is vital. Cracks in the foundation, uneven settling, or changes in soil moisture near the home should be reported and investigated promptly. Regular maintenance checks by professionals can help catch these issues early, ensuring that any necessary repairs are made before they become costly problems.


In conclusion, long-term monitoring and maintenance of tree root influence on soil suction near homes require a proactive approach. By conducting regular assessments, maintaining safe planting distances, pruning roots when necessary, installing barriers, and educating homeowners, we can protect the structural integrity of homes and ensure a safe living environment for years to come.

Architectural honesty and failure is a facet of design that handles the capability of a framework to sustain a designed architectural lots (weight, force, etc) without damaging, and includes the study of past architectural failings in order to protect against failings in future layouts. Structural integrity is the ability of a thing—-- either a structural element or a framework containing lots of components—-- to hold together under a lots, including its very own weight, without breaking or warping exceedingly. It guarantees that the building will certainly execute its created function throughout affordable usage, for as lengthy as its desired lifetime. Things are constructed with structural stability to prevent devastating failing, which can lead to injuries, extreme damages, fatality, and/or financial losses. Structural failure describes the loss of structural honesty, or the loss of load-carrying architectural capability in either a structural element or the framework itself. Structural failure is initiated when a product is stressed out beyond its stamina limit, creating fracture or too much deformations; one restriction state that need to be represented in architectural style is ultimate failure toughness. In a well-designed system, a localized failing needs to not create prompt or even progressive collapse of the whole framework.

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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

[edit]
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

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  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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