| الملخص | تناول البحث اربعة انواع من الفولاذ هي : (St 52-3 , Notronic 32, X82WMoCrV6 54 , 105Cr4) وبنسب كاربون مختلفة : , (0.06,0.105,0.809,0.907) درس سلوك الانبعاج لها تحت تاثير حمل ديناميكي (ضغط – لي ) . الاعمدة قيد البحث كانت دائرية المقطع بقطر (10mm) وبطول (,(400 mm علمت هوية المعادن المراد استخامها بعد تحليلها و معرفة خواصها الميكانيكية في قسم المختبرات والفحص الهندسي في المعهد المتخصص للصناعات الهندسية . جهاز الانبعاج الموجود في احد مختبرات الجامعة التكنولوجية استخدم في تنفيذ الجزء العملي من البحث و توصل الى ان ثابت العمود Cc)) يتناسب عكسيا مع مقاومة الانبعاج بينما نسبة النحافة فيه لاتتغير , كما ان زيادة نسبة الكاربون تزيد الخواص الميكانيكية الى حد معين وان تغير نسبة الكاربون يوثرالى حد ما على عدد دورات الانبعاج ,كما ان سلوك الانبعاج الدوراني ممكن ان يمثل بمعادلة اويلر كحالة ثابتة.
Abstract
In this investigation four type of a steel alloy (St 52-3 , Notronic 32, X82WMoCrV6 5 4 , 105Cr4) with different carbon content (0.06,0.105,0.809,0.907) were buckling under dynamic loading (compression –torsion ) . The column used had constant slenderness ratio. A buckling test-rig was use for carrying out the experimental part of this work .The main conclusion derived from this study is, carbon content increasing will increase the mechanical property up to a limit value and its slightly effected the cyclic buckling . The cyclic bucking behavior (critical dynamic buckling load) may be described by Euler formula as in static case.
Key
Buckling Behavior, Carbon Content, Buckling test rig, slenderness ratio.
Introduction
A machine part subjected to an axial compressive force is called a strut. A strut may horizontal, inclined or even vertical. But a vertical strut is known as a column .The machine members that must be investigated from column action are piston rods, connecting rods, value push rods, screw jack ,side links of toggle jack…etc .It has been observed that when column or strut is subjected to a compressive load and the load is gradually increased , a stage will reach when the column will be subjected to ultimate load . Beyond this , the column will fail by crushing and the load will be known as crushing load. It has also been experienced that sometimes, a compression member doesn't fail entirely by crushing, but also by bending .i.e buckling .This happens in the case of long column. The load, at which the column just buckling is called buckling load, critical load or crippling load and the column is said to have developed on elastic instability. The connecting rod Fig (1) between the hydraulic cylinder and the ram must be designed as a column because it is a relatively long ,slender compression member .What shape should the cross section of the connecting rod be ? From what material should it be made? How is it to be connected to the ram and to the hydraulic cylinder? A column tend to buckle about the axis for which the radius of gyration and the moment of inertia are minimum. Fig (2) show a sketch of a column that has a rectangular cross-section the expected baulking axis is Y-Y because both I and r much smaller than from the X-X axis The term and fixity refer to the manner in which the ends of a column are supported. The most important variable is the moment of restraint offered at the end of the column to the tendency for rotation .Three form of end restraint are pinned ,fixed and free .Fig.(3) shows the effective for these three cases .
Fig (1) Waste paper compactor after Fig (2) Buckling of a thin rectangular column (a)
general appearance of The buckling column (b )
radius of gyration for Y-Y a xis.(c) radius of
gyration For X-X axis after
Fig (3) Values of K for effective length , Lc=KL ,for different end
Connections after
Experimental work
1.Specimen preparation
Round-type steel alloy specimen with a diameter of 10mm a gauge length of 400mm were tested under room temperature and compression-torsion buckling loads. In order to investigated the effect of carbon percentage on the bucking life, four types of steel alloy were selected with different carbon percentage. These alloys are widely used in various industry applications . the Experimental work and the Buckling test rig was done in the department of electromechanical engineering at the University of Technology.
2.Buckling test rig Compression –Torsion.
This work focus on torsion and Compression system together, be used the following steps:
1- The specimen should be contacted horizontally so that the first end of it which is nearer to the electrical motor of torsion system should be fixed, while the other end can be pine.
2- The dial gauge located in position that touches the center of the specimen length.
3-Operation the electric motor with a low speed (17 r.p.m) generates the torque of (T) value, when the torsion stress value (τ) can be obtained.
4-An axial compression is gradually applied on the specimen by a hydraulic pump of compression system.
5- Once a deflection of (1%) of the specimen length is recorded by the dial gauges ,then the electrical motor is switch-of , and the pressure must be released. the experiment test is over .
6- By the end of the experiment test ,the test –rig reading are directly recorded ,the number of cycles of failure from the speed counter ,the pressure of compression from the hydraulic pump buckling load .fig (4,5) show the column before and after buckling
Fig (4) Before Buckling Fig (5) After Buckling
Results analysis
Two methods for analyzing straight, centrally loaded columns are presented,
The Euler formula for long slender columns and J.B.Johnson formula for short columns. The choice of which method to use depends on the value of the actual slenderness ratio for the column being analyzed in relation to the transition slenderness ratio ,or column constant ,Cc ,defined as Cc = √( 2π2E/σ y)
Where ( E ) is the modules of elasticity of the material of the column and ( σ y ) is the yield strength of the material .
Procedure for analyzing straight, centrally loaded columns :
1. From the given column,can compute its actual slenderness ratio.
2. Copulation of the value Cc .
3. Comparing Cc with slenderness ratio KL/r , because Cc represented the value of slenderness ratio that separates along column from a short one ,the result of the comparison indicates which type of analysis should be used .
4. If KL/r is greater than Cc ,the column is long ,used Euler's formula which may be take the form Pcr = π2EAI/(KL)2A = π2EI/( KL)2
Where ( Pcr) is the critical load and (A) is the cross-sectional area of the column and (r) is the radius of gyration ,( r=√ I/A and r2=I/A , I is the moment of inertia) ,
Notice that the buckling load is dependent only on the geometry (length and cross-section) of the column and the stiffness of the material represented by the modules of elasticity.
Discussion
According to Euler formula , the static buckling load is depending only on the geometry (length and cross-section ) of the column and the stiffness of the material represented by the modulus of elasticity .The load or critical load for short column is affected by the strength of the material in addition to its stiffness ,E, while strength is not factor for long column when the Euler formula is used [ 1] .The present work attempted to investigate the effect of carbon content on dynamic buckling i.e. the buckling life . The value of the column constant Cc , is dependent on the material properties of modules of elasticity and the yield strength as shown in fig(6)
Fig (6) The column constant Cc with material properties
For any given class of material ,for example ,steel ,the modulus of elasticity is nearly constant .Thus ,the value of Cc varies inversely as square root of the yield strength while the slenderness ratio behavior is kept constant with varying yield strength as shown in fig (6) .
Carbon content and mechanical properties:
Barsom investigated the effect of carbon content on the mechanical properties of the different type of steel alloy which demonstrates the effect on tensile strength for steel with different carbon equivalent value .The data show TMCP(thermo –mechanical control processes ) may be used to increase strength at agiven carbon value .However decreasing carbon content alone decreases the strength of the base metal .
Chao -Nan Wei studied the effect of carbon content on the tensile stength for 68ILC super alloy and the experimental result indicated that increasing carbon contant from(0.11 % wt) to( 0.15%wt) improves the mechanical strength about (6%) from 1003 Mpa to 1065 Mpa , yield strength from 945 Mpa to 997 Mpa . This finding is in well agreement with the present results as shown in fig (7) .
Sommer etal studded the cyclic deformation and stress-strain behavior of pure α- iron. The influent of small carbon content on cyclic harding was also investigated. The results showed that small carbon content gave less fatigue life than higher carbon percentage .The present results of cyclic buckling showed the same conclusion which
in fig ( 8 )
Fig ( 7 )effect of carbon percentage on the Fig ( 8 )effect of carbon percentage on
yield sttres the buckling cycles to failure
It is clear that ,fig (8) ,the variation cyclic buckling with carbon content is not high.This mean the carbon content slightly effected on cyclic buckling .
Conclusion
1. The column constant is inversely proportional with yield strength for the present steel alloy while the slenderness ratio is not change.
2. Carbon increasing will increase the mechanical property up to a limit value .
3. The carbon content is slightly effected the cyclic buckling.
4. The cyclic bucking behavior (critical dynamic buckling load) may be described by Euler formula as in static case .
Reference
1. Barsom J.M." High Performance Steel And Their Use In Structure " proceeding of the internal symposium of high performance steels for structural application ,(1995)
2. Chao –Nan Wei " The effect of Carbon Content On micros truer and elevated temperature Tensile strength Of Nickel –Brase- Super alloy " Material Science and engineering 3741-3747 (2010).
3. Sommer C .Mug hrabi H. and lochuer D "Influence of temperature and carbon content on cyclic deformation and fatigue behavior of α-Iron " A cat mater . vol .46, 1537-1546 (1998) . | en_US |
