Cory,
What I said was not incorrect, but thank you for sending me back to the textbooks (and the internet) to research and review what I learned almost 40 years ago, and have taken for granted ever since.
If I changed the last word in my first paragraph above to "characteristics" instead of "forces" it might make my point more clear.
What israelkk said in response to my post is partially correct, with respect to the forces, but not with respect to the modulus of elasticity being equal for the two bolts.
I do not dispute that the force on the joint would be the same, given the same torque and "k" factors. The "stretch," a term commonly used in industry for elongation of bolts, however is another matter.
First lets deal with the modulus of elasticity (E), or Young's Modulus, which is the ratio between an applied stress, and the strain (elongation) that results. As a ratio, it is the function of the slope of the straight line portion of the stess strain curve, before plastic deformation occurs. (Everything herein pertains only to elastic deformation, or "stretch")
There are a plethera of sources for E for a variety of materials, steel in the case of the bolt material of this thread, and they are generally denoted as "average," "typical," or "representative", depending on the source. They vary from reference to reference, and sometimes even within the same reference.
Shigley, in the 1963 edition of "Mechanical engineering Design" states the average E for carbon steel as 28.5 X 10*6, and 27.6 X 10*6 for 18-8 SS in Appendix A, table A-1. This same table states the "average" E for gray cast iron (CI) as 14.5, while table A-4 gives a range of E's for gray cast iron, ranging from 11-18 X 10*6 psi.
Van Vlack, in "Elements of Material Science" second edition, states the value of the E for a variety of carbon and stainless steels, as well as gray (and white) CI in appendix C as 30 X 10*6 (across the board). But in an example problem in the text, chapter 1, page 3, he states the average E for steel as 29.5 X 10*6. In another place on page 142, he states the average E for steel as 30 X 10*6. Which is it?
He goes further (in explaining this average value) in the same paragraph to state that the E for iron crystals range from 18-41 X 10*6 psi, depending upon orientation with respect to a uniaxial force.
In a psu.edu reference listed at the end, E ranges from 28.6 to 30 X 10*6.
So, we can see from the literature that even the "average" E for steel is not consistant. E is generally given as an average in order to compare it with the average E of other materials, such as Al, CU, Ti, etc.
E is a function of the modulus of rigidity, (G) or shear modulus, and poissons ratio, (v). So, as these vary within a given metallurgy, E varies. The modulus of elasticity, E, is defined as E=2G(1+v).
G and v are affected by tensile strength which is generally associaated with hardness in steels. Strength is a measure of the ability of a material to resist stress, so it follows that as a material is rated higher in strength, the resistance to stress is going to increase, and the corresponding elongation due to a specific stress is going to be less, resulting in a different stress/strain ratio, and hence a different curve, and a different E.
Table A-4 in Shigley, which is for CI, rather than steel, shows how E increases incrementally from 11-18 X 10*6 psi through a range of 6 types of CI, (ASTM 20, 25, 30, 35, 40, & 50) as hardness ranges from 110 - 250 BHN, and tensile strength ranges from 20 - 50 K psi.
Frankly, I never found such a stand alone table for carbon steel, but it is obvious from many listings of various carbon steel alloys that as tensile strength (and hardness) increase, elongation (in 2 in), and reduction in area of the fracture point decrease, indicating that the corresponging E, G, and v values are not equal.
Now, back to my comments in my post above. A good reference I found that gives a comparison of the relative strengths (as well as hardness) of Metric 8.8 and 12.9 bolts is:
A good place for me to make my point with visual aids is on the fifth page down, figure 2.2.2 of:
Two observations about the values presented on this page.
First, it is clear that the slopes of the stress strain relationship of a variety of steels presented (again, pertaining to the elastic region only) is not identical, indicating that the E for these steels is, in fact, different.
Second, in order to re-state my case, lets look at the two different curves for the same metal, specifically in this case, SAE 3140, one in a 190K psi strength, and the other in a 240K psi strength.
Note first that the slope of the elastic portion of the curve is different.
But for the point that I made, imagine, if you will, that the 8.8 and 12.9 bolts in question in the original post of the thread are of this SAE 3140 material. Let the 190K value represent the E curve for the 8.8 and the 240K value represent the E curve for the 12.9.
What I said was that if the joint was designed to require the fastener to be elongated (stretched) to within a certain percentage (we will use 90%, proof strength here) of the elastic limit, then the approximate force on this joint would be 190 x 0.9 = 171K psi with the 8.8 bolt. The elongation of the bolt can be read directly from the graph. (I used the proof strength of 90% rather than 80% of elastic limit so as to be in the elastic region in order to be able to make my point.)
Now, if a stronger 12.9 bolt of this same material is substituted, and torqued to the same value so as to produce the same force on the joint, no elongation occurs at all, because elongation in this material does not begin until approx 220K psi of stress.
So, to restate my case, if a joint requires that the bolt be "stretched" for joint integrity reasons, substituting a higher strength fastener, and torqueing it to the same torque as the lower strength bolt will not produce the same aamount of stretch, (if any at all in this case.)
Two types of joints that require "stretching" of the fasteners that occur to me right away are (1) a joint where the fastener and the joint material have a different coefficient of thermal expansion over a given temperature range, and the "stretching" of the bolt insures that tension is always maintained on the joint throughout the temperature range, and (2) a joint that might have a gasket material that was expected to further compress (with process induced force or temparature) after being placed in service, and in order to maintain tension on the joint upon returning to the original temperature, so the bolts are "stretched" to a predetermined value.
It is clear from my exercise, that while the value of E given in a lot of references hovers around 30 X 10*6, that this value of E can not be taken carte blanche for any material for the purposes of a statement such as the one made by israelKK above.
Other interesting references I found on this topic include:
I thouroughly enjoyed the mental exercise. Thanks!!
rmw
