I am conducting torsional testing on bone samples and I would like to know what maximum torque relates to? I know that stiffness is related to the degree to mineralization but I can't find any information on maximum torque.
Any input will be greatly appreciated. Thank you!
When any solid piece of matter is submitted to the effect of a force (a load), its structure is somewhat deformed, generally in an elastic way, i.e. being able to give back the energy employed in its deformation and to recover its initial size/shape if unloaded. The resut of it is the manifestation of a reacting, opposite force to that deforming the structure, exactly of the same value (Newton Law). The whole force developed by the deformed structure is employed in two different things: 1. to generate the elastic reaction to the deformation (the structural "stiffness" - the half-full glass) and 2. to induce the deformation (the half-empty glass).
The stiffer the structure, the greater the force needed to deform it. Notably, the induced force will be always equal to the opposite force generated by the structure(Newton). This relationship is linear in the so-called "elastic" bodies (i.e. a rubber ball), but some structures react "elastically-plastically" to defoming forces. "Plastic" behavior means that the body is not yet able to mantain the physical integrity of its structure, i.e. it begins to develop "cracks", and is no more able to recover its size/shape if unloaded (as a piece of clay). In this condition, the ability of the structure to counteract the deforming force is reduced, and the price for this is paid by a higher deformability (lesser stiffness). To note: the deformation of the solid structure under the action of a force, is the price paid by the system to follow always strictly the Newon Law. In fact, the deforming force and the reacting force will be always the same (Newton).
Technically, it can be told that, during the "plastic" behavior of a structure which is progressively deformed by a force, the relaitonship between the induced deformation and the magnitude of the interacting forces grows up.
When one performs a mechanical test, the apparatus submits the assayed body to a constantly progressing deformation by exerting on it a very great force that could be regarded as infinite. So, the deformation proceeds inevitably linearly with time, regardless of the magnitude of the reaction force opposed by the deformed structure. The apparatus measures, and describes as a graph, the reacting force opposed by the strcture (y) as a function of the constantly growing deformation (time, x).
When studying an elastic-plastic body (as most of bodies in Nature), the apparatus gives a linear relaitonship between force (F, y) and deformation (d, x) ("elastic" behavior) during a certain time, depending of the ability of the structure of the body to stand deformation without suffer any crack. Of course, the more the deformation increases, the higher the chance to develop a crack. This can proceed in two different ways:
1. Suddenly during the elastic behavior. In this case, the linear F/d relationship is suddenly interrupted, and the graph comes down vertically up to y=0, i.e. expressing that no more force is opposed by the structure despite of any increase in "deformation". Obviously, the structure has been broken into pieces, and the pieces can not yet been further deformed. This behavior is described as "brittle", i.e. "easy to get totally cracked after it underwent the first crack" (as that of glass or marble, or a dry branch of a tree), as opposed to "tough" ("hard to complete the fracture process after showing the first crack (as a fresh bone, a piece of steel, or a green branch of a tree).
2. Slowly, by being progressively deformed, showing a graphical decline of the F/d curve after the end of the linear relationship ("yield point"). The graph usually grows up (slower than before, of course) during a certain increase of deformation (x), until reaching a maximum, corresponding to the maximal force the structure can oppose anyway in the assayed conditions. Afterwards the opposed force generally decreases, more or less suddenly depending on the kind of matter the structure is made of, until reaching zero (fracture of the structure, as in "1"). This behavior is described as "Plastic", as referred to above.
In any of these two cases, it can be said that the deformed structure "suffers" proportionally to the magnitude of the force it is able to oppose to the deforming load. This kind of mechanical "suffering" is called "stress". Stress can be expressed mathematically by the simple ratio between the magnitude of the deforming force F (in any of the two senses, remember that they are the same - Newton) and that of he coss-sectional area A of the structure which is perpendicularly affected by that force: stress = F/A.
Also in any of the two cases described, there is always a maximal value adopted by the opposed force (y) to the load induced by the machine. This maximal F, divided by the cross-sectional area A of the structure perpendicular to the force direction at that moment, will express the "maximal stress" the system can manifest. Importantly, the force opposed by the structure at the very moment of fracture is zero (!); thus, the "fracture load" would be always zero. In order to avoid this incongruence, the "maximal stress" (always a non-zero value, obviously) is taken as the best representative of the "resistance to fracture" (maximal strength) of the structure in the assayed conditions. The assayed structure can be told to have that "maximal stress" as a physical characteristic as an expression of its resistance to fracture in the assayed conditions. In a nutshell, "maximal stress defines maximal strength in the assayed conditions".
The above is valid regardless of the way the structure is deformed by the force: compression, traction, bending, shear, torsion.
Now, let's give a look to torsion. If the deforming load induces a "torsion stress" ( = torsion F/A) on the structure, the definition of its strength can be perfectioned a little. The deforming force F is now regarded as acting in a direction which is tangential to the structure on a certain peripheral point of it. Thus, the force F effectively acting on the structure would correspond to the so-called "torsional moment" (moment = force times distance) effectively exerted on the structure. The torsional moment in a given condition should be expressed by multiplying the magnitude of the force F times the distance d of the reference point to the center of rotation of the system. Well, this product is called... Torque !, and is usually expreessed in N (Newtons, a good name for the unit, indeed!) x m:
Torque (N) = F (tangential at a point, in N) x d (from that point to center of mass, in m).
Let's transpor now this definition of Torque to the mechanical testing ot the body, assuming now that it is being deformed in torsion. Then, we will have the following equivalences:
Maximal stress (F/A) = resistance to fracture = maximal (Torque / A) value.
This is the way to define "maximal torque" in a drastic situation (falling of the structure). It is no necessary to do it as such, however. I have selected this method to induce the concept just to be sure that also some other elementary mechanical concepts are also learnt concomittantly. In fact, you can also define the Torque, even in the same example, as calculated at any point of the test, with no need at all to breack the structure out. Yet, you can define the "maximal" torque in this situation only by extending the example up to the falling point.
Importantly, in those systems in which there is a limitation to the torque produced, could be also no need to face any disruption of the structure, and however you can also have a "maximal torque". For instance, you can describe the maximal torque produced in the system [rudder / rudder driver] in a boat during a storm (no need for the rudder to be broken), the same way as you have calculated torque in the above example. In fact, the most frequent use of the "maximal torque" concept is the definition of the "maximal rotational force" a motor can transmit to the driven axle.
When any solid piece of matter is submitted to the effect of a force (a load), its structure is somewhat deformed, generally in an elastic way, i.e. being able to give back the energy employed in its deformation and to recover its initial size/shape if unloaded. The resut of it is the manifestation of a reacting, opposite force to that deforming the structure, exactly of the same value (Newton Law). The whole force developed by the deformed structure is employed in two different things: 1. to generate the elastic reaction to the deformation (the structural "stiffness" - the half-full glass) and 2. to induce the deformation (the half-empty glass).
The stiffer the structure, the greater the force needed to deform it. Notably, the induced force will be always equal to the opposite force generated by the structure(Newton). This relationship is linear in the so-called "elastic" bodies (i.e. a rubber ball), but some structures react "elastically-plastically" to defoming forces. "Plastic" behavior means that the body is not yet able to mantain the physical integrity of its structure, i.e. it begins to develop "cracks", and is no more able to recover its size/shape if unloaded (as a piece of clay). In this condition, the ability of the structure to counteract the deforming force is reduced, and the price for this is paid by a higher deformability (lesser stiffness). To note: the deformation of the solid structure under the action of a force, is the price paid by the system to follow always strictly the Newon Law. In fact, the deforming force and the reacting force will be always the same (Newton).
Technically, it can be told that, during the "plastic" behavior of a structure which is progressively deformed by a force, the relaitonship between the induced deformation and the magnitude of the interacting forces grows up.
When one performs a mechanical test, the apparatus submits the assayed body to a constantly progressing deformation by exerting on it a very great force that could be regarded as infinite. So, the deformation proceeds inevitably linearly with time, regardless of the magnitude of the reaction force opposed by the deformed structure. The apparatus measures, and describes as a graph, the reacting force opposed by the strcture (y) as a function of the constantly growing deformation (time, x).
When studying an elastic-plastic body (as most of bodies in Nature), the apparatus gives a linear relaitonship between force (F, y) and deformation (d, x) ("elastic" behavior) during a certain time, depending of the ability of the structure of the body to stand deformation without suffer any crack. Of course, the more the deformation increases, the higher the chance to develop a crack. This can proceed in two different ways:
1. Suddenly during the elastic behavior. In this case, the linear F/d relationship is suddenly interrupted, and the graph comes down vertically up to y=0, i.e. expressing that no more force is opposed by the structure despite of any increase in "deformation". Obviously, the structure has been broken into pieces, and the pieces can not yet been further deformed. This behavior is described as "brittle", i.e. "easy to get totally cracked after it underwent the first crack" (as that of glass or marble, or a dry branch of a tree), as opposed to "tough" ("hard to complete the fracture process after showing the first crack (as a fresh bone, a piece of steel, or a green branch of a tree).
2. Slowly, by being progressively deformed, showing a graphical decline of the F/d curve after the end of the linear relationship ("yield point"). The graph usually grows up (slower than before, of course) during a certain increase of deformation (x), until reaching a maximum, corresponding to the maximal force the structure can oppose anyway in the assayed conditions. Afterwards the opposed force generally decreases, more or less suddenly depending on the kind of matter the structure is made of, until reaching zero (fracture of the structure, as in "1"). This behavior is described as "Plastic", as referred to above.
In any of these two cases, it can be said that the deformed structure "suffers" proportionally to the magnitude of the force it is able to oppose to the deforming load. This kind of mechanical "suffering" is called "stress". Stress can be expressed mathematically by the simple ratio between the magnitude of the deforming force F (in any of the two senses, remember that they are the same - Newton) and that of he coss-sectional area A of the structure which is perpendicularly affected by that force: stress = F/A.
Also in any of the two cases described, there is always a maximal value adopted by the opposed force (y) to the load induced by the machine. This maximal F, divided by the cross-sectional area A of the structure perpendicular to the force direction at that moment, will express the "maximal stress" the system can manifest. Importantly, the force opposed by the structure at the very moment of fracture is zero (!); thus, the "fracture load" would be always zero. In order to avoid this incongruence, the "maximal stress" (always a non-zero value, obviously) is taken as the best representative of the "resistance to fracture" (maximal strength) of the structure in the assayed conditions. The assayed structure can be told to have that "maximal stress" as a physical characteristic as an expression of its resistance to fracture in the assayed conditions. In a nutshell, "maximal stress defines maximal strength in the assayed conditions".
The above is valid regardless of the way the structure is deformed by the force: compression, traction, bending, shear, torsion.
Now, let's give a look to torsion. If the deforming load induces a "torsion stress" ( = torsion F/A) on the structure, the definition of its strength can be perfectioned a little. The deforming force F is now regarded as acting in a direction which is tangential to the structure on a certain peripheral point of it. Thus, the force F effectively acting on the structure would correspond to the so-called "torsional moment" (moment = force times distance) effectively exerted on the structure. The torsional moment in a given condition should be expressed by multiplying the magnitude of the force F times the distance d of the reference point to the center of rotation of the system. Well, this product is called... Torque !, and is usually expreessed in N (Newtons, a good name for the unit, indeed!) x m:
Torque (N) = F (tangential at a point, in N) x d (from that point to center of mass, in m).
Let's transpor now this definition of Torque to the mechanical testing ot the body, assuming now that it is being deformed in torsion. Then, we will have the following equivalences:
Maximal stress (F/A) = resistance to fracture = maximal (Torque / A) value.
This is the way to define "maximal torque" in a drastic situation (falling of the structure). It is no necessary to do it as such, however. I have selected this method to induce the concept just to be sure that also some other elementary mechanical concepts are also learnt concomittantly. In fact, you can also define the Torque, even in the same example, as calculated at any point of the test, with no need at all to breack the structure out. Yet, you can define the "maximal" torque in this situation only by extending the example up to the falling point.
Importantly, in those systems in which there is a limitation to the torque produced, could be also no need to face any disruption of the structure, and however you can also have a "maximal torque". For instance, you can describe the maximal torque produced in the system [rudder / rudder driver] in a boat during a storm (no need for the rudder to be broken), the same way as you have calculated torque in the above example. In fact, the most frequent use of the "maximal torque" concept is the definition of the "maximal rotational force" a motor can transmit to the driven axle.
Dear Zophia
This article may be useful for you
Acta Orthop Scand. 1976 Jun;47(3):257-63.
Experimental measurement of maximum torque capacity of long bones.
Strömberg L, Dalén N.
Abstract
By means of a new method with high precision (error 3.1 percent), the maximum torque capacity of an entire long bone from an experimental animal was measured under standardized conditions within 10 minutes after sacrifice of the animal.
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