BackgroundIn Brazil, crack cocaine use remains a healthcare challenge due to the rapid onset of its pleasurable effects, its ability to induce craving and addiction, and the fact that it is easily accessible. Delayed action on the part of the Brazilian Government in addressing the drug problem has led users to develop their own strategies for surviving the effects of crack cocaine use, particularly the drug craving and psychosis. In this context, users have sought the benefits of combining crack cocaine with marijuana. Our aim was to identify the reasons why users combine crack cocaine with marijuana and the health implications of doing so. MethodsThe present study is a qualitative study, using in-depth interviews and criteria-based sampling, following 27 crack cocaine users who combined its use with marijuana. Participants were recruited using the snowball sampling technique, and the point of theoretical saturation was used to define the sample size. Data were analyzed using the content analysis technique.
ResultsThe interviewees reported that the combination of crack cocaine use with marijuana provided “protection” (reduced undesirable effects, improved sleep and appetite, reduced craving for crack cocaine, and allowed the patients to recover some quality of life). ConclusionsCombined use of cannabis as a strategy to reduce the effects of crack exhibited several significant advantages, particularly an improved quality of life, which “protected” users from the violence typical of the crack culture.Crack use is considered a serious public health problem in Brazil, and there are few solution strategies. Within that limited context, the combination of cannabis and crack deserves more thorough clinical investigation to assess its potential use as a strategy to reduce the damage associated with crack use. Characteristics of the sampleThe sample, which contained 27 crack cocaine users between the ages of 19 and 49 years (mean 25.9), consisted mostly of 21- to 30-year-old males who had received little education (only elementary school), belonged to a low social class (class E) , were unemployed, were living in shelters or on the street without family and were crack cocaine -dependent. All of the participants proved to be crack cocaine -dependent according to DSM-IV criteria, and nearly 70% of them were also reported to be marijuana -dependent.Drug use was not always recreational. All of the participants in the sample reported having had problems with some of the drugs cited, but crack cocaine was the drug that most affected all aspects of their lives. Social problems, such as robberies and loss of family, job, and social status, were most commonly cited, followed by physical injuries resulting from assaults, impaired appearance, etc.
The processes used by some crack cocaine manufacturers, however, introduce impurities resulting in a product less pure than the powder cocaine from which it was derived.47 With respect to doses, one gram of powder cocaine generally yields five to ten doses, whereas one gram of crack cocaine yields two to ten doses.
Cravings and transient paranoid symptoms were described as the effects of the drug that most contributed to these damages.The participants reported having used various self-devised strategies to either stop crack cocaine use or overcome the problems caused by it, including seeking help in religion, avoiding contact with crack cocaine users, and the use of other drugs combined with crack cocaine. Combination with other drugsAccording to the interviewees’ statements, the combination of crack cocaine and marijuana was not the only drug combination used. Even sporadically, drugs, such as alcohol, hallucinogens ( Ecstasy), and snorted cocaine, and medications, such as benzodiazepines, were also used in combination with crack cocaine in an attempt to either increase the pleasurable effects or minimize the unpleasant effects. However, as with the combination of crack cocaine and marijuana, the combination with alcohol was also mentioned often.The criteria used to choose a drug to be combined with crack cocaine were based on the experience of other users, experimentation, and the individual evaluation of the effects of the combination tested. Reasons cited for combining crack cocaine with marijuanaBased on the interviewees’ statements, it became evident that in the context of crack cocaine use, the participants attributed a “protection” role to marijuana that was revealed in several ways.Reduction of unpleasant effects: The participants attributed relaxing properties to marijuana, which interfered with the effects of crack cocaine by decreasing those effects that were considered to be undesirable. Additionally, participants considered that the effects resulting from the combination were pleasant. Transient paranoid symptoms, which are a typical effect of crack cocaine use and according to users can cause fear, distrust, and sometimes violent behavior, were the effects that were most commonly mentioned by the interviewees as being suppressed in the presence of marijuana.
When I mix marijuana with crack, the effect of marijuana is stronger than the effect of crack cocaine, which then curbs paranoia (psychosis) and controls cravings (G38MC).The “mesclado” (“mix”) makes me fly. It takes away the wickedness of the rock. I do not look for pieces of rock on the ground, like a fool.
The effect of the “mesclado” is better; it is very different (V43MC).Reduction of crack cocaine-seeking behavior: The serenity caused by marijuana helped the participants control their cravings so that the desire to smoke was reduced. Because of this effect, strategies to obtain the drug, such as thefts and robberies, did not need to be used, which protected the users from possible fatalities resulting from these activities.
The participants stated that marijuana caused a type of “numbness” of the mind, which made them “forget” about crack cocaine, even if only temporarily. The focus on crack cocaine was displaced by the effects resulting from the combination. The pure rock makes me aggressive because I want to smoke more, and if someone stops me from doing this, I become violent, even if it is a family member.
With marijuana, I control this situation because I am more relaxed, less anxious. (G24M) Quality of lifeParticipants also reported that the combination of the two drugs allowed for the partial recovery of the quality of life that was lost with crack cocaine use. Basic human needs that were previously compromised by the use of crack cocaine were regained with the use of marijuana combined with crack cocaine.
Sleep, hunger, and sex are examples of this well-being that were cited by the interviewees. It lasts longer. Assuming that I smoke a crack cocaine rock that costs 10 Brazilian reais (approximately $5) in a half hour, with marijuana, it will take one hour. I split it into small bits, I stop, and then I smoke more.” (R27M)The combination of crack cocaine with marijuana was not always perceived as beneficial by the user. Those who disliked the combination of crack cocaine with marijuana attributed this dislike to the reasons outlined below.Decrease in the potency of the drug: A small number of participants did not consider the combination of crack cocaine with marijuana to be beneficial; specifically, the action of marijuana on the effects of crack cocaine (i.e., reducing its intensity) was not well accepted by everyone. The calm and relaxation promoted by the combination that represented a gain for some of the participants was the cause of displeasure for others, so that the participants started using the “mesclado”, but after a period of time, they went back to smoking crack cocaine alone, without combining it with marijuana.
If I smoke some marijuana, I do not feel good. I feel depressed.
I feel very bad. I think it is because I used too much crack, so it affected my brain a bit. If I smoke a joint today, I feel worse than if I had smoked a rock.
I feel very depressed. (M23F) The sequence of the marijuana and crack cocaine combinationThe sequence of the marijuana and crack cocaine combination seemed to be of great importance in the effects resulting from combining the two drugs. Some of the participants preferred to use marijuana before smoking crack cocaine, whereas others preferred to use it after smoking crack cocaine, but the simultaneous use of marijuana and crack cocaine was most commonly observed in this sample (“mesclado” or “pitilho”). Simultaneous use of marijuana and crack cocaine (mesclado)As mentioned previously, the “mesclado” was the preferred manner of combining these two drugs. The participants attributed this preference to several factors, which are outlined below.Does not attract attention on the street: According to the interviewees, smoking from a pipe makes crack cocaine use obvious; they are identified as users anywhere they use a crack pipe. Using a cigarette, in which marijuana is mixed with the rock (crack cocaine), is more “protective”.
These users face no discrimination because they are not identified as crack cocaine users (known as a “craqueiro” in Brazil). Additionally, some of the interviewees stated that the unpleasant effects, mainly the transient paranoid symptoms, disappeared, and the combined use of marijuana and crack cocaine also helped them to remain calmer, which contributed to greater social acceptance and consequently decreased the high degree of marginalization to which they were subjected. I can smoke in a park without any problem. Using only the rock, I get paranoid (psychotic), suspicious of everyone. I just want to be hidden from view.
I think about stealing all the time. (R31M)The interval between consumption is increased: The interviewees stated that when they smoked the “mesclado”, it took longer for them to want to smoke it again, resulting in them consuming a smaller amount of crack cocaine. With the “mesclado”, 1 to 2 h elapsed before they repeated the drug use; in contrast, when they used only crack cocaine, this period of time was reduced to 5 or 10 min. Use of marijuana before crack cocaineA few interviewees reported using marijuana before crack cocaine because they claimed that in such circumstances, they became more relaxed and calmer and would not consume crack cocaine afterwards while they experienced this tranquility. Some of the interviewees revealed that the only way to change this condition was to consume alcohol to “break” this state and then return to smoking crack cocaine after marijuana use. These implications led them to stop using marijuana in this manner, replacing it with other manners of use, the most common of which was the “mesclado”. Use of marijuana after crack cocaineMarijuana was used in this sequence with the same goal as that of the previous sequence, which was the reduction of the undesirable effects of crack cocaine.
Those who consumed marijuana after crack cocaine reported that it prevented them from seeking more crack cocaine to continue using it. I smoked it marijuana afterwards to stop, understand? Because after the effect of marijuana that was it! Then, I was relaxed.” (C33M)Some users reported a slightly different goal: after they had consumed all of the crack cocaine and did not have the possibility of getting more of the drug, they smoked marijuana to abolish the desire to smoke more crack.It is important to highlight that in this sample, combinations with other drugs were aimed at reducing the undesirable effects of crack cocaine and allowing the users to smoke it in a calmer manner. Accordingly, with the exception of one user, none of the participants attempted to replace crack cocaine with another drug (in this case, marijuana).
Despite the positive results promoted by the use of marijuana before crack, some of the interviewees altered the sequence of this combination due to the unfavorable environment created by this drug, which made the use of crack cocaine more difficult. The present study examined the combination of crack cocaine and cannabis as an informal alternative to cope with the use of crack cocaine. This combination has been previously mentioned in other studies by Brazilian authors –,.The study sample consisted mainly of young men of low socioeconomic status, with little schooling, who were living on the street.
These characteristics are consistent with the profile of Brazilian crack users recently described by the government. Thus, the study findings are likely reflective of the broader population of crack users in Brazil given the similarities in characteristics noted here.In their narratives, the interviewees described the benefits of the cannabis-crack combination. A reduced craving, which is considered the main cause of dependence and involvement in high-risk situations to obtain the drug , was one of the advantages most often mentioned by the participants. In a study conducted with a convenience sample of six users undergoing treatment, Andrade et al. found that a reduced craving was the greatest benefit of using the crack-cannabis combination. Participants in the present study additionally reported a reduction of transient paranoid symptoms, which sometimes lead to violence , , as a positive outcome of the combination.The interviewees emphasized that the improved quality of life as a result of eliminating or reducing cravings and paranoid symptoms was the most positive effect of using the cannabis-crack combination. This effect protected them from marginalization and/or violent environments, which are the main causes of death, favoring the reduction of their marked vulnerability in the crack cocaine use culture.
Additionally, a persistent relationship with society is highly valuable in terms of potential access to healthcare services, which might help improve their wellbeing. This combination also resulted in decreasing crack cocaine-seeking behavior, which in turn reduced use of crack cocaine, increased monetary savings, and increased survival. The unhealthy appearance of crack cocaine users due to drug-induced appetite inhibition was compensated for by marijuana use, which awakened the appetite, causing weight gain, and also improved sleep.The most common combination mentioned by other authors and the present study participants involved adding crack rocks to marijuana inside of a cigar. However, in this study, they also reported other methods of drug intake, such as using cannabis before or after crack. In either case, the interviewees slowed or even stopped their crack use due to the state of relaxation induced by cannabis. It is worth noting that participants were not always pleased with the outcome because their focus was not on quitting crack. Nevertheless, these types of combinations should be given more attention in strategies based on the replacement of drugs associated with multiple physical and mental complications by less damaging drugs.The therapeutic effects of cannabis have been known for a long time.
Carlini et al. and Leite and Carlini et al.
, in the 1980s, demonstrated the medicinal properties of marijuana, especially the anticonvulsant properties of the drug.Webb et al. observed 100 patients who were using cannabis for medicinal purposes, and the authors obtained significant results, including the fact that 50% of the patients experienced reduced levels of stress and anxiety, 45% experienced improved sleep, and 12% experienced improved appetite.
.OverviewFracture mechanics is a methodology that is used to predict and diagnose failure of a part with an existing crack or flaw. The presence of a crack in a part magnifies the stress in the vicinity of the crack and may result in failure prior to that predicted using traditional.The traditional approach to the design and analysis of a part is to use strength-of-materials concepts. In this case, the stresses due to applied loading are calculated.
Failure is determined to occur once the applied stress exceeds the material's strength (either yield strength or ultimate strength, depending on the criteria for failure).In fracture mechanics, a is calculated as a function of applied stress, crack size, and part geometry. Failure occurs once the stress intensity factor exceeds the material's. At this point the crack will grow in a rapid and unstable manner until fracture. Fracture mechanics is important to consider for several important reasons:. Cracks and crack-like flaws occur much more frequently than might be expected.
Cracks can either pre-exist in a part, or they can develop due to high stress or. Typically, as the strength of a material increases, fracture toughness decreases. The intuition of many engineers to prefer higher strength materials can lead them down a dangerous path. Ignoring fracture mechanics can lead to failure of parts at loads below what is expected using a strength-of-materials approach. A failure due to brittle fracture is rapid and catastrophic and provides little warning.The image below shows the SS Schenectady tanker, one of the World War II Liberty Ships and one of the most iconic fracture failures.
The Liberty ships all had a tendency to crack during cold weather and rough seas, and multiple ships were lost. Approximately half of the cracks initiated at the corners of the square hatch covers which acted as stress risers. The SS Schenectady split in two while sitting at dock. An understanding of fracture mechanics would have prevented these losses.Image Source:Stress Concentrations Around CracksCracks act as stress risers and cause the stress in the part to spike near the tip of the crack. As a simple example, consider the case of an elliptical crack in the center of an infinite plate.
Where σ is the nominal stress and ρ is the radius of curvature of the ellipse, ρ = b 2/a.As the radius of the crack tip approaches zero, the theoretical stress approaches infinity. This infinite stress is known as a stress singularity and is not physically possible. Instead, the stress distributes over the surrounding material, resulting in plastic deformation in the material at some distance from the crack tip. This region of plastic deformation is called the and is discussed in a later section. The plastic deformation causes blunting of the crack tip which increases the radius of curvature and brings the stresses back to finite levels.Because of the stress singularity issues that arise when using the stress concentration approach, and because of the plastic zone that develops around the crack tip which renders the stress concentration approach invalid, other methods have been developed for characterizing the stresses near the tip of the crack. The most prevalent method in use today is to calculate a, as discussed in a later section. Modes of LoadingThere are three primary modes that define the orientation of a crack relative to the loading.
A crack can be loaded in one mode exclusively, or it can be loaded in some combination of modes.Image Source:The figure above shows the three primary modes of crack loading. Mode I is called the opening mode and involves a tensile stress pulling the crack faces apart. Mode II is the sliding mode and involves a shear stress sliding the crack faces in the direction parallel to the primary crack dimension. Mode III is the tearing mode and involves a shear stress sliding the crack faces in the direction perpendicular to the primary crack dimension.Engineering analysis almost exclusively considers Mode I because it is the worst-case situation and is also the most common.
Cracks typically grow in Mode I, but in the case that the crack does not start in Mode I it will turn itself to become Mode I, as illustrated in the figure below. Where a is the crack size and Y is a dimensionless geometry factor that is dependent on the geometry of the crack, the geometry of the part, and the loading configuration.It is important to note that because equations describing the linear-elastic stress field were used to develop the stress intensity factor relationship above, the concept of the stress intensity factor is only valid if the region of plastic deformation near the crack tip is small. This will be discussed in more detail.Stress Intensity Factor SolutionsThe difficult part of calculating the stress intensity factor for a specific situation is finding the appropriate value of the dimensionless geometry factor, Y. This geometry factor is dependent on the geometry of the crack, the geometry of the part, and the loading configuration. A classic case is plate with a crack through the center, as shown below. The stress intensity factor for a specific situation can be found through numerical methods such as Finite Element Analysis (FEA). However, solutions for many cases can be found in the literature.
Solutions for some common cases, including the case shown above, can be found on our page.Superposition for Combined LoadingBecause the concept of the stress intensity factor, the stress intensity factor solutions can be combined by superposition to find solutions to more complex problems. For example, the stress intensity factor solution for a single edge cracked plate in tension can be combined with the solution for a single edge cracked plate in bending, as shown in the figure below.
Fracture ToughnessA material can resist applied stress intensity up to a certain critical value above which the crack will grow in an unstable manner and failure will occur. This critical stress intensity is the fracture toughness of the material. The fracture toughness of a material is dependent on many factors including environmental temperature, environmental composition (i.e. Air, fresh water, salt water, etc.), loading rate, material thickness, material processing, and crack orientation to grain direction.
It is important to keep these factors in mind when selecting a fracture toughness value to assume during design and analysis.Fracture toughness values for many common engineering materials.Fracture Toughness vs. ThicknessFracture toughness decreases as material thickness increases until the part is thick enough to be in a.
Above this plane-strain thickness, the fracture toughness is a constant value known as the plane-strain fracture toughness. The plane-strain fracture toughness in Mode I loading is of primary interest, and this value is denoted by K IC.The fracture toughness for a material at a specific thickness can be approximated as.
Even though the fracture toughness can be approximated as a function of the thickness of the part, it is still a good idea to use the plane-strain fracture toughness value in design and analysis.Fracture Toughness vs. StrengthIn general, within a specific class of materials, fracture toughness decreases as strength increases. If you start with a block of material and heat treat it and work it to increase the strength properties, you will also typically reduce the fracture toughness of the material.The figure below shows fracture toughness vs. Material strength for various classes of materials.
It can be seen that for many materials, particularly for the and the, fracture toughness decreases with increasing strength.Image Source:Fracture Toughness vs. Crack OrientationThe fracture toughness of a material typically varies as a function of the crack orientation with respect to the grain direction. Because of this, fracture toughness values are typically reported along with the crack orientation.The possible combinations of crack orientation and grain direction are shown in the figure below for both a rectangular shape and a cylindrical shape.
Two-digit codes are used to denote the crack orientation. The first digit indicates the direction normal to the crack face. The second digit indicates the direction of the crack path.
Source: MIL-HDBK-5JInitial Crack SizeCracks and crack-like flaws are common in engineering materials. Cracks will typically form around pre-existing flaws which act as stress concentrations and which, upon high stress or, develop into full-fledged cracks. Many flaws are serious enough that they should be treated as cracks, and these include deep scratches, inclusions of foreign particles, and grain boundaries. In addition to material flaws, geometric features in a part which act as stress concentrations can lead to crack initiation, including notches, holes, grooves, and threads.
Cracks can also initiate from flaws introduced through other failure mechanisms, such as from pitting due to corrosion or from abrasion due to galling.Determining the initial size of the crack is critical to assessing the potential for fracture. A conservative approach is to select a non-destructive evaluation (NDE) method for inspecting the part under consideration, and then to assume that a crack equal in size to the minimum detectable flaw size exists in the part in the most highly stressed location.Many references are available that provide minimum detectable flaw sizes for various NDE methods, one of which is NASA-STD-5009. A table from NASA-STD-5009 is shown below for US units, along with a corresponding figure that provides the definitions of the crack dimensions 'a' and 'c'. Plastic Zone Size Plane-Stress vs. Plane-StrainThe size of the plastic zone is dependent on whether the part is considered to be in a plane-stress or a plane-strain condition.
In plane-stress, the section is thin enough that the stresses through the thickness of the section are approximately constant. In plane-strain, stresses develop through the thickness of the section to resist contraction of the material and to keep the strain throughout the thickness approximately constant.The part can be considered to be in plane-strain if the thickness satisfies the following condition. Where K app is the stress intensity due to applied stress, and S ty is the material's tensile yield strength.For the actual plastic zone size to be equal to the theoretical plastic zone size, the stresses in the plastic zone must substantially exceed the material's yield strength.
Because the yielded material in the plastic zone cannot support stresses much above the yield stress, the stresses near the crack tip are redistributed to the material farther out, and therefore the true size of the plastic zone is larger than the theoretical predicted value. The actual size of the plastic zone is approximately equal to 2r t, so a more realistic estimate of the plastic zone size, r p, is given. Note that the plastic zone size is proportional to (K app/S ty) 2. This indicates that the plastic zone will be smaller for higher strength materials. Additionally, higher toughness materials are able to develop higher stress intensities before fracture, so the plastic zone will grow larger in higher toughness materials before failure occurs.
Materials with low tensile strength and high fracture toughness can develop very large plastic zones at the crack tip.Plastic Zone Size for Plane-StrainThe plastic zone size estimates described in the previous section apply to the plane-stress condition where the section is thin enough that the stresses through the thickness of the section are approximately constant. If the section is thick enough to be considered in plane-strain (i.e. Stresses develop through the thickness of the section to resist contraction of the material and to keep the strain throughout the thickness approximately constant), then the size of the plastic zone is reduced as compared to that in the plane-stress condition.The plastic zone size for the plane-strain condition can be approximated as. Where K app is the stress intensity due to applied stress, and S ty is the material's tensile yield strength.Ductile vs. Brittle FractureThere are two frames of reference when discussing ductile fracture versus brittle fracture. These frames of reference are the fracture mechanism and the fracture mode.When materials scientists talk about brittle fracture and ductile fracture, they are typically referring to the fracture mechanism, which describes the fracture event at a microscopic level.
In general, the brittle fracture mechanism is cleavage, and the ductile fracture mechanism is dimpled rupture, also known as microvoid coalescence. The cleavage mechanism is associated with brittle fracture. It involves little plastic deformation, and the fracture surface looks smooth with ridges. The microvoid coalescence mechanism is associated with ductile fracture.
This mechanism involves the formation, growth, and joining of small voids in the material which is enabled through plastic flow, and the fracture surface looks dimpled like a golf ball.When mechanical engineers talk about brittle fracture and ductile fracture, they are typically referring to the fracture mode, which describes the high-level behavior of the material during the fracture event. The figure below illustrates the fracture mode. A load-displacement curve is shown along with cracked specimens placed at various locations along the curve. In the linear region of the curve with lower applied load, the stresses in the part are below the material yield strength. If the part were to fail in this region, this would be referred to as brittle fracture since the part has failed prior to what is predicted using strength-of-materials methods. Note that in this region, the plastic zone around the crack tip (shown in red) will typically be small, and so the linear elastic assumption applies and can be used to analyze the part.
As the load increases, the plastic zone size increases. If the part fails in the higher region of the load-displacement curve, this is referred to as ductile fracture. If the plastic zone size has exceeded the but has not yet extended across the entire section, then elastic-plastic methods such as the can be used to analyze the part.
Once the plastic zone size has extended across the entire section (gross section yielding), fracture mechanics methods can no longer be used, and the section will need to be analyzed using a strength-of-materials approach. Static Fracture Analysis MethodsStatic fracture analysis should be performed considering the peak load that the part is expected to see during its lifetime. In the static analysis methods, the load is steady and does not vary with time.On the other hand, can be used to consider crack growth due to a time-varying load. The loads over the entire service life of the part are typically considered to ensure that the crack will not grow to a critical size.The following sections describe several standard methods for performing static fracture analysis. The topic of fatigue crack growth is.Linear Elastic Fracture Mechanics (LEFM)Linear elastic fracture mechanics (LEFM) uses the concept of the, K, discussed previously.
The stress intensity factor at the crack tip is calculated and then compared to the critical stress intensity of the material. The, K IC, is typically chosen as the value of critical stress intensity to use for design and analysis.
The factor of safety is then calculated as. Where K app is the stress intensity factor at the crack tip due to applied stress.Applicability of LEFMLinear elastic fracture mechanics (LEFM) assumes that the material is behaving in a linear-elastic manner. For this assumption to be valid, the must be small relative to the part and crack geometry. If the plastic zone size extends too close to bounds of the part, then the situation approaches gross yielding of the section.The plastic zone is situated just ahead of the crack tip. In general, the tip of the crack must be a distance of at least d LEFM from any part boundary, where d LEFM is defined below. Note that d LEFM is equal to 4 times the.
Where σ app is the applied stress, K app is the stress intensity at the applied stress, S ty is the material's tensile yield strength, and K IC is the material's plane-strain fracture toughness.Plot the design point ( S r, K r) for the current load case on the FAD diagram and ensure that it falls within the FAD failure locus. To calculate the factor of safety, draw a line from the origin through the design point and continue this line until it intersects the FAD failure locus. This line is called the load line.
The factor of safety is the ratio of the length of the load line between the origin and the design point, and the length of the load line between the origin and the failure point. In the figure above, the design point falls within the FAD failure locus, and the factor of safety is approximately 3.0.In the figure above, notice that the failure locus for LEFM is shown as a dotted horizontal line, and that the FAD failure locus falls beneath the LEFM locus. This indicates that the failure predictions made using LEFM are under-conservative. The reason for the reduced failure locus in the FAD curve is that the plasticity near the crack tip increases the effective crack length and thus increases the severity of the crack situation.Notice also that the failure locus for plastic collapse (i.e. The failure locus that is predicted using strength-of-materials methods) is shown as a vertical dotted line.
The FAD failure locus crosses through the plastic collapse locus and then pushes to the right, which indicates that the part is gaining strength. Accounts for this apparent strength increase.It is helpful to make a note of which of the 'naive' failure loci the load line intersects. If the load line intersects the LEFM failure locus, then the part strength is limited by fracture for the load case under consideration, so it will fail by fracture before it yields. If the load line intersects the failure locus for plastic collapse, then the part strength is limited by yielding for the current load case.The FAD failure locus is defined. Where E is the material's elastic modulus, S ty is the material's tensile yield strength, and S r is the stress ratio as defined above. The value ε ref is the true strain corresponding to the stress S rS ty, and it can be calculated using the.Note that the FAD failure locus is a function only of stress ratio, S r. Every other parameter in the equation defining the failure locus is a constant material property.
To build the locus, sweep through a range of stress ratios from 0 up to a maximum stress ratio corresponding to that at the material's.A final point to consider about the FAD approach is that it can account for material plasticity while still using linear-elastic stress intensities. This allows for the simplicity of the FAD method and is a major advantage over other elastic-plastic methods.Residual Strength CurveThe residual strength curve shows the strength of the part as a function of crack size. If no crack is present, the part strength is equal to the material yield strength. However, as the crack grows, the strength (i.e. The amount of stress that can be withstood before failure) is reduced.A residual strength curve for an example case is shown in the figure below. This case is for a 2-inch wide plate with a center through crack and a material with a yield strength of 145 ksi and a plane-strain fracture toughness of 60 ksi.in 0.5. The residual strength curve is shown in red.
For a given crack size, any stress value above this curve results in failure. To evaluate acceptability of a design, plot the design point ( a, σ app) for the current case, where a is the crack length and σ app is the applied combined stress.
Draw a vertical line up to the residual strength curve - this intersection represents the failure point if the crack size is held constant but the stress in increased to the critical (failure) point. Draw another vertical line horizontally to the residual strength curve - this intersection represents the failure point if the stress is held constant but the crack size is increased to the critical (failure) point. The factors of safety for each of these failure conditions can then be calculated:Factor of safety on critical stress. It is important to note that in general, the geometry factor, Y, is a function of the crack size. So, as the crack size is varied, the value of Y will also vary. Generally, the value of Y will peak as the crack size becomes large relative to the part dimensions, which explains why the residual strength curve drops down to a critical stress value of 0 at the boundary of the part.It is also important to note that as the crack size approaches 0, the theoretical critical stress approaches infinity.
This is clearly unrealistic, since the tensile strength of the material provides an upper limit on the stress that the material can withstand. To correct the residual strength curve in the small-crack region, a straight line is drawn between the material's tensile yield strength and the tangent point on the theoretical critical stress curve. In some cases it is impossible to find a tangent point. In this situation, provides guidance that the transition point between the straight-line curve and the theoretical critical stress curve can be taken at the point where the theoretical critical stress is equal to 2/3 of the material's tensile yield strength.Fatigue Crack GrowthThis page on fracture mechanics covered the analysis of cracked parts under static load conditions (i.e. Conditions with steady loads that do not vary with time). For the case where the load does vary with time, the stress intensity at the crack tip will also vary. The crack will grow in the case that the variance in stress intensity exceeds the material's threshold stress intensity.
The growth of a crack under conditions of varying stress intensity is called fatigue crack growth, and it described in our page.