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      Grindability and Hardness tests            
                           
      5 Hardness tests:              
      5.1 Mohs scale of mineral hardness:            
        - This scale was created in 1812 by the German geologist and mineralogist Friedrich Mohs.    
        - The Mohs scale is used to determine the relative hardness of minerals from ten well-defined minerals of 
          varying hardness.              
        - This scale (nonlinear) is graduated from 1 to 10 (1 is the lowest hardness and 10 is the highest hardness).
        - The principle of this scale is based on the fact that a mineral can scratch another if its own hardness is higher.
        - Mohs hardness scale:              
         
     
               
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
        - Because the Mohs scale is a nonlinear scale, the difference between the hardness of a diamond and that of a corundum
          is much greater than the difference in hardness between calcite and gypsum.      
        - As an example, diamond (10) is about 4-5 times harder than corundum (9), which is about 2 times harder than topaz (8).
        - An other example, with your fingernail (2,5 of hardness), you can scratch gypsum but not calcite.  
        - Other usual Mohs values:            
         
     
     
           
           
           
           
           
           
           
           
           
           
           
           
           
           
           
           
           
        - Usual objects used to find materials hardness:          
         
     
             
                   
                   
                   
                   
                   
                   
      5.2 Intensive indentation hardness tests:            
        - These are the most commonly performed tests.          
        - The principle is always the same: a deformable indenter leaves an imprint in the material to be tested.  
        - Measuring the dimensions of the imprint and one deduces the hardness.      
        - The most well known are: Vickers, Brinell and Rockwell hardness tests.      
        - Vickers hardness measurement is made with a normalized pyramidal point diamond with a square base and an apex 
          angle equal to 136°.              
        - The Brinell test consists of pushing (applying a force F) a penetrator having a spherical diameter D, generally 
            a polished carbide, in a metal in order to deduce its hardness.        
        - Rockwell hardness tests are tests of penetration. There are actually different types of penetrators which consist of 
           a diamond cone or a polished hardened steel ball.          
        - These tests will not be detailed here because few used in the field of cement industry.    
        - Examples of testers:              
         
     
     
     
       
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
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      5.3 JK Drop Weight Test:              
        - The JK Drop Weight test has been developed at the Julius Kruttschnitt Mineral Research Centre in Brisbane (Australia)
          in the early 1990s.              
        - Web address: http://www.jkmrc.uq.edu.au/          
        - This test is used extensively worldwide in the mining industry as a key ore characterisation test.  
        - The test produces parameters which are used in comminution circuit design and optimization,   
          especially for AG/SAG mills circuits.            
        - These parameters are called A and b, where A is the asymptote of a plot of specific energy against T10  
          (% of product below 10% of the feed size) and b is a measure of the slope in the following equation:  
         
     
                   
                           
          where Ecs is the specific energy in kWh/t.          
        - The minimum quantity of sample required for testing is 100 kg of crushed rock in the -63+13,2 mm size range.
        - Different energy inputs are tested at different fraction ranges of 13,2 to 63 mm on the ore. From that, A and B are known.
        - By varying the height and the mass of the drop weight, a very large range of energy inputs can be generated.
        - Representations of the JK Drop Weight Tester:          
         
     
           
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
         
     
             
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
        - Reference values of JK test:            
         
     
     
           
           
           
           
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      5.4 Slegten hardness Test:              
        - The Slegten hardness test was specifically developed to determine the hardness of clinkers in the cement industry.
          In other words, this test measures the breakability of the material.      
        - There is some similarity with the JK Drop Weight test.        
        - The principle is to drop a steel ball on a grain of clinker in order to know the energy required to break this grain.
        - Before the test, 40-50 grains of clinker having a size between 9 and 10 mm are selected on the feed belt
          at the ball mill entrance.              
        - A picture with clinker grains of 9-10mm:          
         
     
             
                   
                   
                   
                   
                   
                   
                   
                   
                   
        - This size was chosen because it was the most common clinker grains size.      
        - One measures the potential energy to crush this pieces of 9-10mm with a ball of 32,6 gr by measuring the height
          of the drop.                 
        - If a grain doesn't break at a certain height, a new test at the next higher height is realized. The energy calculated is 
          the sum of the energies required for each height.          
        - The test is realized with 30 grains and the result of the test is the average of the drop heights.  
        - A picture of broken clinker grains:            
         
     
             
                   
                   
                   
                   
                   
                   
                   
                   
                   
        - The result can be expressed in Joules, but it is the average height in cm which is very well known worldwide.
        - Sketch of the Slegten hardness test:            
         
     
             
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
        - This test is also used in the mining industry.          
        - This test is an important help to define the first compartment ball charge gradation of a cement ball mill.
        - A majority of clinkers has a hardness around 120 (cm).        
        - Typical values of the Slegten hardness test:          
         
     
                   
                           
                           
                           
                           
                           
                           
                           
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