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  • Young’s Modulus (Elastic Modulus, Modulus of Elasticity)

    by Esther Mar | Mar 28, 2019

    In the article on Tensile Testing there is brief description of Young’s Modulus (also called the Elastic Modulus or Modulus of Elasticity).  Every now and again a question is raised as to whether it is possible to change this material characteristic, usually because designers are looking for more stiffness in a particular structure.  Hence, a discussion on Young’s Modulus is provided.

    When a metal is subjected to load in a tension test, there is an initial range of loading in which no permanent deformation of the specimen occurs, i.e. if the load is removed at any value within this range, the specimen will return completely to its original dimensions.  This is known as the elastic range.  The data obtained from the tension test is generally plotted as a stress-strain curve.  Within the elastic range of loading the strain produced is directly proportional to the applied stress.  The law of proportionality between stress and strain in the elastic range is known as Hooke’s Law.  The Young’s Modulus is the ratio between the stress that is applied (tensile or compressive) and the elastic strain that results, i.e. it is the slope of the elastic portion of the stress-strain curve and is expressed in units of stress (psi).  The higher the modulus, the more stress is needed to create the same amount of strain, i.e. the higher the modulus the higher the stiffness or rigidity of the material.  Since Young’s Modulus is needed, in conjunction with thickness, for calculating deflection of beams and other members, it is an important design value. 

    Young’s Modulus is determined by the binding forces between atoms.  Since these forces cannot be changed without changing the basic nature of the material, it follows that the Young’s Modulus is one of the most structure-insensitive of the mechanical properties.  It is only slightly affected by alloying additions, heat treatment, cold work, or, in the case of steel, by relatively exotic microstructures such as dual phase.  The tensile Young’s Modulus of ferritic steels is close to 30,000,000 psi at room temperature.  The tensile Young’s Modulus of austenitic stainless steels is about 28,000,000 psi at room temperature. Within each material class there are very small differences. Increasing the temperature decreases the Young’s Modulus.  It decreases linearly to somewhere in the order of 1000oF, depending on material class, and then begins to drop rapidly.

    Because the stress-strain relationship of many materials does not conform to Hooke’s Law throughout the elastic range, there are several methods of defining the Young’s Modulus as a straight line relationship using an approximation such as an initial tangent modulus, a tangent modulus at any stress, a secant modulus between the origin and any stress, and a chord modulus between any two stresses.  An ASTM standard exists for test methods.

    youngmodulus

     

    Although Young’s Modulus is a characteristic of the stress-strain curve, its precise determination using static methods (deflection under load increments in a tension test) requires regard for numerous variables, including the accuracy and the precision of the apparatus used to measure stress and strain, characteristics of the test specimen (such as grain orientation relative to the direction of stress, grain size, residual stress, previous strain history, dimensions and eccentricity), testing conditions (such as alignment of the specimen, speed of testing, temperature, and temperature variations) and interpretation of the test data. Following the ASTM standard ensures far more accurate results than taking the number off a routine stress-strain curve.  However, the more accurate methods are dynamic in nature and are based in induced mechanical vibration or ultrasonic pulses where the mode and period of vibration of a metal specimen are obtained and analyzed.

     

     


  • Springback in sheet metal forming

    by Esther Mar | Dec 17, 2018

    When producing a part, either by deep drawing, stretch forming or bending, flat sheet is transformed into a design shape and dimension.  At the end of the forming process, when the part has been released from the forces of the forming tool, there is a distortion in the shape and dimension of the formed part.  This distortion is termed springback.  A depiction of springback in a simple bend can be seen in Figure 1.

    Springback is inherent in sheet metal forming.  It can be can be understood by looking at a material’s stress stain curve (discussed in the module on Tensile Testing) which characterizes the behavior of metal under applied force.  During forming, the material is strained beyond the yield strength in order to induce permanent deformation.  When the load is removed, the stress will return to zero along a path parallel to the slope of the elastic portion of the curve, which is the elastic modulus.  This can be seen in Figure 2.  The permanent deformation will therefore be less than what is designed into the part unless springback is factored in.

    Springback is dependent on various material characteristics but can be affected by tooling design.  The most important parameters are elastic modulus, strength, thickness, and bend radius.  Other material characteristics, especially YPE, can also be important.

    Material with a higher elastic modulus will show less springback than material with a lower elastic modulus.  This can be seen in Figure 2, where the unloading stress strain curve would be shifted toward less springback if it had a higher slope.  However between different types of steel there is essentially no difference in the elastic modulus so unless a totally different material is chosen, such as aluminum, this is not a consideration.

    A material with a higher yield strength will have a greater ratio of elastic to plastic strain and will exhibit more springback than material with a lower yield strength for a given amount of strain.

    Thickness is important because of how it impacts on strain.  There is high total strain involved in bending a thick material around a given radius and low total strain involved in bending a thin material around the same radius.  While under load, the total strain consists of both elastic and plastic strains.  When the total strain is high, based on the stress strain curve, the relative amount of elastic strain is low.  When the total strain is low, the relative amount of elastic strain is high and this results in more springback.  It can be imagined that a very thin material could be bent around a radius with zero plastic strain.  In this case the strain would be so low that it would be entirely elastic and the material would completely spring back to its original shape after the load is removed. Conversely a very thick material being bent over the same radius would show a very high total strain.  The absolute value of the elastic portion of the strain would be similar to that of the thin material but it would be insignificant compared to the plastic portion of the strain.  Therefore the thick material would show very little springback. 

    Another material characteristic worth mentioning is the Yield Point Elongation (YPE).  YPE is the strain associated with discontinuous yielding that can occur when steel is placed in tension.  It is well demonstrated that steel showing a pronounced YPE shows less springback that steel with no YPE. In the case of steel with a high YPE more of the stress is used to concentrate thinning locally resulting in a lower proportion of total strain that is elastic and hence less springback.  One would think that this parameter can be used to effectively reduce springback.  However that is not always the case because YPE is variable, between coils, within coils, and is directional, so its effects can be variable.  In general variability can be more problematic than the absolute value of springback.

    Methods of addressing springback include process design and part design.  In terms of the process, overbending, retarding metal flow due by use of draw beads and higher binder pressure, using lower press speeds, restriking, applying tension during bending, using tighter die clearances, are all techniques that are used.  In terms of part design, by utilizing tooling configurations that force higher strain over a small area springback can be minimized.

    As well there are angle compensation feedback mechanisms that are able to make automatic adjustments for each piece.

    Finally there are modeling techniques that attempt to analyze three dimensional parts so that the tooling can be designed to compensate for springback. 

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    Figure 1.  Elastic Springback  (the change in the angle from start to finish of the forming process)

                      (r = radius, a = angle, s = start, f = finish)      

    spring2
     Figure 2.  Strain and Stress Behaviour During the Forming Process
  • I-Units – A Standard for Determining Flatness

    by Esther Mar | Aug 29, 2018

    Flatness can be a confusing subject.  People know when they see a shape condition that will give them trouble but they sometimes don’t describe it accurately and often don’t specify their requirement in a meaningful way.  The industry uses terms such as commercial flat, half standard, flatness critical, restricted flatness or panel flat but these terms are vague.  ASTM standard specifications contain flatness tolerances that are only based on maximum deviation from a horizontal flat surface, although they do refer to two alternative methods for flatness determination, I-Units and % Steepness, contained in ASTM A1030.

    I-Units is an exacting quantitative flatness measurement.  It is a dimensionless number that incorporates both the height (H) and peak to peak length (L, or P in the diagram below) of a repeating wave.

    iunits

    The formula for I-Units is as follows:        

    I = [(3.1415 x H)/2L]2 x 10

    Simplified, I = 2.467[H/L]2 x 105

    For example:  a sheet with a 1/16” high wave which repeats every 12” would have an I-Unit value of 6.7.

    There are several charts on the internet that provide the calculated values for a given H and L.


  • Mils vs. Microns

    by Esther Mar | Aug 22, 2018

    milsvsmicrons

    Mil -
    A unit of measurement in the English system that is measured in thousandths of an inch.

    (i.e., .001″ = one thousandth of an inch or 1.0 mil)

     

    Micron - A unit of measurement in the metric system that is equal to one thousandth of a millimeter.

    (also called a micrometer, abbreviated ‘μm’)

     

    For the conversion:

    Mils to Microns: (Number of Mils) x 25.4 (i.e., 0.75 mil = 19 microns)

    Microns to Mils: (Number of Microns) / 25.4 (i.e., 14 microns = .55 mil)


  • Transit Abrasion on Galvanized Sheet

    by Esther Mar | Jul 05, 2018

    Galvanized sheet sometimes exhibits a surface imperfection that appears as short black marks, usually in patches.  This condition has several names in addition to transit abrasion including fretting corrosion, friction oxidation, wear oxidation and chafing.  These terms refer to the root cause of the problem, which is related to friction between contact points, similar to galling. The condition is characterized by a mirror image on the reverse side of the sheet. The reason the term corrosion or oxidation is used is that this imperfection is associated with the buildup of oxide particles.

    Fretting corrosion is the most technical name.  It refers to corrosion damage at the high points of contact surfaces.  It occurs under load, under conditions of repeated relative motion of the surfaces in contact with each other, and these two conditions must be sufficient to produce deformation of the surface, which is likely with galvanized sheet because the zinc coating is fairly soft. This mechanism can affect any two surfaces that are not intended to move against each other and, in the case of machinery, can prematurely wear out parts.

    Fretting corrosion has been observed on galvanized steel in both coil form and bundles of cut lengths.  This condition is never seen on the galvanizing line, almost always being found in a customer’s plant.  The repeated motion comes from vibrations that occur during shipment of the product.  The condition is rare in the case of truck shipments, generally being prevalent when product is transported by train and ship where it incurs vibrations for long periods of time. The load comes from the weight of the coil (or stack of sheets).  This is why transit abrasion is observed mostly on the outer portion of the coil at the bottom half of it (or bottom portion of the bundle).

    There are measures that can prevent or minimize transit abrasion, all targeting reducing load or minimizing friction.  Actions that are very effective are designing support saddles to reduce concentrated point loading on the bottom of coils and avoiding stacking during transit.  Other measures are reducing the coil size and oiling the material, although these methods are not always practical or possible.

    There are two mechanisms that operate to produce fretting corrosion:  wear-oxidation and oxidation-wear. The first proposes that cold welding occurs at the contact points with small fragments of metal being removed and that these immediately oxidize.  The second proposes that the normal oxide layer already present on the galvanized sheet is ruptured at the high points under load and vibration, thus producing oxide particles. 

    Fretting corrosion is a cosmetic condition. There is no evidence that it is detrimental to the corrosion resistance of the galvanized sheet.

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    transit2